Daily Papers

Machine Learning Force Fields (MLFFs) are a promising alternative to expensive ab initio quantum mechanical molecular simulations. Given the diversity of chemical spaces that are of interest and the cost of generating new data, it is important to understand how MLFFs generalize beyond their training distributions. In order to characterize and better understand distribution shifts in MLFFs, we conduct diagnostic experiments on chemical datasets, revealing common shifts that pose significant challenges, even for large foundation models trained on extensive data. Based on these observations, we hypothesize that current supervised training methods inadequately regularize MLFFs, resulting in overfitting and learning poor representations of out-of-distribution systems. We then propose two new methods as initial steps for mitigating distribution shifts for MLFFs. Our methods focus on test-time refinement strategies that incur minimal computational cost and do not use expensive ab initio reference labels. The first strategy, based on spectral graph theory, modifies the edges of test graphs to align with graph structures seen during training. Our second strategy improves representations for out-of-distribution systems at test-time by taking gradient steps using an auxiliary objective, such as a cheap physical prior. Our test-time refinement strategies significantly reduce errors on out-of-distribution systems, suggesting that MLFFs are capable of and can move towards modeling diverse chemical spaces, but are not being effectively trained to do so. Our experiments establish clear benchmarks for evaluating the generalization capabilities of the next generation of MLFFs. Our code is available at https://tkreiman.github.io/projects/mlff_distribution_shifts/.

Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFFs, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as O(n^3) to O(n^7), with n proportional to the number of basis functions. To address this issue, we propose a multi-stage computational framework -- ASTEROID, which lowers the data cost of MLFFs by leveraging a combination of cheap inaccurate data and expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting tahe potential bias of this data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model's accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabeled. Extensive experiments on MD datasets and downstream tasks validate the efficacy of ASTEROID. Our code and data are available at https://github.com/abukharin3/asteroid.

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

Polymers are a versatile class of materials with widespread industrial applications. Advanced computational tools could revolutionize their design, but their complex, multi-scale nature poses significant modeling challenges. Conventional force fields often lack the accuracy and transferability required to capture the intricate interactions governing polymer behavior. Conversely, quantum-chemical methods are computationally prohibitive for the large systems and long timescales required to simulate relevant polymer phenomena. Here, we overcome these limitations with a machine learning force field (MLFF) approach. We demonstrate that macroscopic properties for a broad range of polymers can be predicted ab initio, without fitting to experimental data. Specifically, we develop a fast and scalable MLFF to accurately predict polymer densities, outperforming established classical force fields. Our MLFF also captures second-order phase transitions, enabling the prediction of glass transition temperatures. To accelerate progress in this domain, we introduce a benchmark of experimental bulk properties for 130 polymers and an accompanying quantum-chemical dataset. This work lays the foundation for a fully in silico design pipeline for next-generation polymeric materials.

Point defects play a central role in driving the properties of materials. First-principles methods are widely used to compute defect energetics and structures, including at scale for high-throughput defect databases. However, these methods are computationally expensive, making machine-learning force fields (MLFFs) an attractive alternative for accelerating structural relaxations. Most existing MLFFs are based on graph neural networks (GNNs), which can suffer from oversmoothing and poor representation of long-range interactions. Both of these issues are especially of concern when modeling point defects. To address these challenges, we introduce the Accelerated Deep Atomic Potential Transformer (ADAPT), an MLFF that replaces graph representations with a direct coordinates-in-space formulation and explicitly considers all pairwise atomic interactions. Atoms are treated as tokens, with a Transformer encoder modeling their interactions. Applied to a dataset of silicon point defects, ADAPT achieves a roughly 33 percent reduction in both force and energy prediction errors relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.

Simulating atomic-scale processes, such as protein dynamics and catalytic reactions, is crucial for advancements in biology, chemistry, and materials science. Machine learning force fields (MLFFs) have emerged as powerful tools that achieve near quantum mechanical accuracy, with promising generalization capabilities. However, their practical use is often limited by long inference times compared to classical force fields, especially when running extensive molecular dynamics (MD) simulations required for many biological applications. In this study, we introduce BoostMD, a surrogate model architecture designed to accelerate MD simulations. BoostMD leverages node features computed at previous time steps to predict energies and forces based on positional changes. This approach reduces the complexity of the learning task, allowing BoostMD to be both smaller and significantly faster than conventional MLFFs. During simulations, the computationally intensive reference MLFF is evaluated only every N steps, while the lightweight BoostMD model handles the intermediate steps at a fraction of the computational cost. Our experiments demonstrate that BoostMD achieves an eight-fold speedup compared to the reference model and generalizes to unseen dipeptides. Furthermore, we find that BoostMD accurately samples the ground-truth Boltzmann distribution when running molecular dynamics. By combining efficient feature reuse with a streamlined architecture, BoostMD offers a robust solution for conducting large-scale, long-timescale molecular simulations, making high-accuracy ML-driven modeling more accessible and practical.

Molecular dynamics (MD) simulations are essential tools for unraveling atomistic insights into the structure and dynamics of condensed-phase systems. However, the universal and accurate prediction of macroscopic properties from ab initio calculations remains a significant challenge, often hindered by the trade-off between computational cost and simulation accuracy. Here, we present ByteFF-Pol, a graph neural network (GNN)-parameterized polarizable force field, trained exclusively on high-level quantum mechanics (QM) data. Leveraging physically-motivated force field forms and training strategies, ByteFF-Pol exhibits exceptional performance in predicting thermodynamic and transport properties for a wide range of small-molecule liquids and electrolytes, outperforming state-of-the-art (SOTA) classical and machine learning force fields. The zero-shot prediction capability of ByteFF-Pol bridges the gap between microscopic QM calculations and macroscopic liquid properties, enabling the exploration of previously intractable chemical spaces. This advancement holds transformative potential for applications such as electrolyte design and custom-tailored solvent, representing a pivotal step toward data-driven materials discovery.

Accurate and scalable machine-learned inter-atomic potentials (MLIPs) are essential for molecular simulations ranging from drug discovery to new material design. Current state-of-the-art models enforce roto-translational symmetries through equivariant neural network architectures, a hard-wired inductive bias that can often lead to reduced flexibility, computational efficiency, and scalability. In this work, we introduce TransIP: Transformer-based Inter-Atomic Potentials, a novel training paradigm for interatomic potentials achieving symmetry compliance without explicit architectural constraints. Our approach guides a generic non-equivariant Transformer-based model to learn SO(3)-equivariance by optimizing its representations in the embedding space. Trained on the recent Open Molecules (OMol25) collection, a large and diverse molecular dataset built specifically for MLIPs and covering different types of molecules (including small organics, biomolecular fragments, and electrolyte-like species), TransIP attains comparable performance in machine-learning force fields versus state-of-the-art equivariant baselines. Further, compared to a data augmentation baseline, TransIP achieves 40% to 60% improvement in performance across varying OMol25 dataset sizes. More broadly, our work shows that learned equivariance can be a powerful and efficient alternative to equivariant or augmentation-based MLIP models.

Creating a single unified interatomic potential capable of attaining ab initio accuracy across all chemistry remains a long-standing challenge in computational chemistry and materials science. This work introduces a training protocol for foundation machine-learning interatomic potentials (MLIPs) that bridge molecular, surface, and materials chemistry through cross-domain learning. First, we introduce enhancements to the MACE architecture that improve its performance on chemically diverse databases by increasing weight sharing across chemical elements and introducing non-linear factors into the tensor decomposition of the product basis. Second, we develop a multi-head replay post-training methodology that enables efficient knowledge transfer across diverse chemical domains. By fine-tuning on datasets at different levels of electronic structure theory, including inorganic crystals, molecular systems, surface chemistry, and reactive organic chemistry, we demonstrate that a single unified model achieves state-of-the-art performance across several chemical domains. Comprehensive benchmarking reveals superior cross-domain transferability compared with existing specialised and multi-task models, with notable improvements in molecular and surface properties while maintaining state-of-the-art performance in materials-property prediction.

Machine Learning Interatomic Potentials (MLIP) are a novel in silico approach for molecular property prediction, creating an alternative to disrupt the accuracy/speed trade-off of empirical force fields and density functional theory (DFT). In this white paper, we present our MLIP library which was created with two core aims: (1) provide to industry experts without machine learning background a user-friendly and computationally efficient set of tools to experiment with MLIP models, (2) provide machine learning developers a framework to develop novel approaches fully integrated with molecular dynamics tools. The library includes in this release three model architectures (MACE, NequIP, and ViSNet), and two molecular dynamics (MD) wrappers (ASE, and JAX-MD), along with a set of pre-trained organics models. The seamless integration with JAX-MD, in particular, facilitates highly efficient MD simulations, bringing MLIP models significantly closer to industrial application. The library is available on GitHub and on PyPI under the Apache license 2.0.

Machine learning-based interatomic potentials and force fields depend critically on accurate atomic structures, yet such data are scarce due to the limited availability of experimentally resolved crystals. Although atomic-resolution electron microscopy offers a potential source of structural data, converting these images into simulation-ready formats remains labor-intensive and error-prone, creating a bottleneck for model training and validation. We introduce AutoMat, an end-to-end, agent-assisted pipeline that automatically transforms scanning transmission electron microscopy (STEM) images into atomic crystal structures and predicts their physical properties. AutoMat combines pattern-adaptive denoising, physics-guided template retrieval, symmetry-aware atomic reconstruction, fast relaxation and property prediction via MatterSim, and coordinated orchestration across all stages. We propose the first dedicated STEM2Mat-Bench for this task and evaluate performance using lattice RMSD, formation energy MAE, and structure-matching success rate. By orchestrating external tool calls, AutoMat enables a text-only LLM to outperform vision-language models in this domain, achieving closed-loop reasoning throughout the pipeline. In large-scale experiments over 450 structure samples, AutoMat substantially outperforms existing multimodal large language models and tools. These results validate both AutoMat and STEM2Mat-Bench, marking a key step toward bridging microscopy and atomistic simulation in materials science.The code and dataset are publicly available at https://github.com/yyt-2378/AutoMat and https://huggingface.co/datasets/yaotianvector/STEM2Mat.

Despite the widespread applications of machine learning force field (MLFF) on solids and small molecules, there is a notable gap in applying MLFF to complex liquid electrolytes. In this work, we introduce BAMBOO (ByteDance AI Molecular Simulation Booster), a novel framework for molecular dynamics (MD) simulations, with a demonstration of its capabilities in the context of liquid electrolytes for lithium batteries. We design a physics-inspired graph equivariant transformer architecture as the backbone of BAMBOO to learn from quantum mechanical simulations. Additionally, we pioneer an ensemble knowledge distillation approach and apply it on MLFFs to improve the stability of MD simulations. Finally, we propose the density alignment algorithm to align BAMBOO with experimental measurements. BAMBOO demonstrates state-of-the-art accuracy in predicting key electrolyte properties such as density, viscosity, and ionic conductivity across various solvents and salt combinations. Our current model, trained on more than 15 chemical species, achieves the average density error of 0.01 g/cm^3 on various compositions compared with experimental data. Moreover, our model demonstrates transferability to molecules not included in the quantum mechanical dataset. We envision this work as paving the way to a "universal MLFF" capable of simulating properties of common organic liquids.

Machine learning interatomic potentials (MLIPs) have revolutionized molecular and materials modeling, but existing benchmarks suffer from data leakage, limited transferability, and an over-reliance on error-based metrics tied to specific density functional theory (DFT) references. We introduce MLIP Arena, a benchmark platform that evaluates force field performance based on physics awareness, chemical reactivity, stability under extreme conditions, and predictive capabilities for thermodynamic properties and physical phenomena. By moving beyond static DFT references and revealing the important failure modes of current foundation MLIPs in real-world settings, MLIP Arena provides a reproducible framework to guide the next-generation MLIP development toward improved predictive accuracy and runtime efficiency while maintaining physical consistency. The Python package and online leaderboard are available at https://github.com/atomind-ai/mlip-arena.

The simulation of large-scale systems with complex electron interactions remains one of the greatest challenges for the atomistic modeling of materials. Although classical force fields often fail to describe the coupling between electronic states and ionic rearrangements, the more accurate ab-initio molecular dynamics suffers from computational complexity that prevents long-time and large-scale simulations, which are essential to study many technologically relevant phenomena, such as reactions, ion migrations, phase transformations, and degradation. In this work, we present the Crystal Hamiltonian Graph neural Network (CHGNet) as a novel machine-learning interatomic potential (MLIP), using a graph-neural-network-based force field to model a universal potential energy surface. CHGNet is pretrained on the energies, forces, stresses, and magnetic moments from the Materials Project Trajectory Dataset, which consists of over 10 years of density functional theory static and relaxation trajectories of sim 1.5 million inorganic structures. The explicit inclusion of magnetic moments enables CHGNet to learn and accurately represent the orbital occupancy of electrons, enhancing its capability to describe both atomic and electronic degrees of freedom. We demonstrate several applications of CHGNet in solid-state materials, including charge-informed molecular dynamics in Li_xMnO_2, the finite temperature phase diagram for Li_xFePO_4 and Li diffusion in garnet conductors. We critically analyze the significance of including charge information for capturing appropriate chemistry, and we provide new insights into ionic systems with additional electronic degrees of freedom that can not be observed by previous MLIPs.

Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model -- and its qualitative and at times quantitative accuracy -- on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, and chemical reactions. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry.

The development of reliable and extensible molecular mechanics (MM) force fields -- fast, empirical models characterizing the potential energy surface of molecular systems -- is indispensable for biomolecular simulation and computer-aided drug design. Here, we introduce a generalized and extensible machine-learned MM force field, espaloma-0.3, and an end-to-end differentiable framework using graph neural networks to overcome the limitations of traditional rule-based methods. Trained in a single GPU-day to fit a large and diverse quantum chemical dataset of over 1.1M energy and force calculations, espaloma-0.3 reproduces quantum chemical energetic properties of chemical domains highly relevant to drug discovery, including small molecules, peptides, and nucleic acids. Moreover, this force field maintains the quantum chemical energy-minimized geometries of small molecules and preserves the condensed phase properties of peptides, self-consistently parametrizing proteins and ligands to produce stable simulations leading to highly accurate predictions of binding free energies. This methodology demonstrates significant promise as a path forward for systematically building more accurate force fields that are easily extensible to new chemical domains of interest.

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are SE(n) equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

Creating fast and accurate force fields is a long-standing challenge in computational chemistry and materials science. Recently, several equivariant message passing neural networks (MPNNs) have been shown to outperform models built using other approaches in terms of accuracy. However, most MPNNs suffer from high computational cost and poor scalability. We propose that these limitations arise because MPNNs only pass two-body messages leading to a direct relationship between the number of layers and the expressivity of the network. In this work, we introduce MACE, a new equivariant MPNN model that uses higher body order messages. In particular, we show that using four-body messages reduces the required number of message passing iterations to just two, resulting in a fast and highly parallelizable model, reaching or exceeding state-of-the-art accuracy on the rMD17, 3BPA, and AcAc benchmark tasks. We also demonstrate that using higher order messages leads to an improved steepness of the learning curves.

Achieving a balance between computational speed, prediction accuracy, and universal applicability in molecular simulations has been a persistent challenge. This paper presents substantial advancements in the TorchMD-Net software, a pivotal step forward in the shift from conventional force fields to neural network-based potentials. The evolution of TorchMD-Net into a more comprehensive and versatile framework is highlighted, incorporating cutting-edge architectures such as TensorNet. This transformation is achieved through a modular design approach, encouraging customized applications within the scientific community. The most notable enhancement is a significant improvement in computational efficiency, achieving a very remarkable acceleration in the computation of energy and forces for TensorNet models, with performance gains ranging from 2-fold to 10-fold over previous iterations. Other enhancements include highly optimized neighbor search algorithms that support periodic boundary conditions and the smooth integration with existing molecular dynamics frameworks. Additionally, the updated version introduces the capability to integrate physical priors, further enriching its application spectrum and utility in research. The software is available at https://github.com/torchmd/torchmd-net.

Science progresses by iteratively advancing and correcting humanity's understanding of the world. In machine learning (ML) research, rapid advancements have led to an explosion of publications, but have also led to misleading, incorrect, flawed or perhaps even fraudulent studies being accepted and sometimes highlighted at ML conferences due to the fallibility of peer review. While such mistakes are understandable, ML conferences do not offer robust processes to help the field systematically correct when such errors are made. This position paper argues that ML conferences should establish a dedicated "Refutations and Critiques" (R&C) Track. This R&C Track would provide a high-profile, reputable platform to support vital research that critically challenges prior research, thereby fostering a dynamic self-correcting research ecosystem. We discuss key considerations including track design, review principles, potential pitfalls, and provide an illustrative example submission concerning a recent ICLR 2025 Oral. We conclude that ML conferences should create official, reputable mechanisms to help ML research self-correct.

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. No systematic strategy currently exists to infer large-scale physical properties of a cell from its many molecular components. This is a significant obstacle to understanding biophysical processes such as cell adhesion and migration. Here, we develop a data-driven biophysical modeling approach to learn the mechanical behavior of adherent cells. We first train neural networks to predict forces generated by adherent cells from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion protein, such as zyxin, are sufficient to predict forces and generalize to unseen biological regimes. This protein field alone contains enough information to yield accurate predictions even if forces themselves are generated by many interacting proteins. We next develop two approaches - one explicitly constrained by physics, the other more agnostic - that help construct data-driven continuum models of cellular forces using this single focal adhesion field. Both strategies consistently reveal that cellular forces are encoded by two different length scales in adhesion protein distributions. Beyond adherent cell mechanics, our work serves as a case study for how to integrate neural networks in the construction of predictive phenomenological models in cell biology, even when little knowledge of the underlying microscopic mechanisms exist.

Identifying and predicting the factors that contribute to the success of interdisciplinary research is crucial for advancing scientific discovery. However, there is a lack of methods to quantify the integration of new ideas and technological advancements in astronomical research and how these new technologies drive further scientific breakthroughs. Large language models, with their ability to extract key concepts from vast literature beyond keyword searches, provide a new tool to quantify such processes. In this study, we extracted concepts in astronomical research from 297,807 publications between 1993 and 2024 using large language models, resulting in a set of 24,939 concepts. These concepts were then used to form a knowledge graph, where the link strength between any two concepts was determined by their relevance through the citation-reference relationships. By calculating this relevance across different time periods, we quantified the impact of numerical simulations and machine learning on astronomical research. The knowledge graph demonstrates two phases of development: a phase where the technology was integrated and another where the technology was explored in scientific discovery. The knowledge graph reveals that despite machine learning has made much inroad in astronomy, there is currently a lack of new concept development at the intersection of AI and Astronomy, which may be the current bottleneck preventing machine learning from further transforming the field of astronomy.

The last few years have seen the development of numerous deep learning-based protein-ligand docking methods. They offer huge promise in terms of speed and accuracy. However, despite claims of state-of-the-art performance in terms of crystallographic root-mean-square deviation (RMSD), upon closer inspection, it has become apparent that they often produce physically implausible molecular structures. It is therefore not sufficient to evaluate these methods solely by RMSD to a native binding mode. It is vital, particularly for deep learning-based methods, that they are also evaluated on steric and energetic criteria. We present PoseBusters, a Python package that performs a series of standard quality checks using the well-established cheminformatics toolkit RDKit. Only methods that both pass these checks and predict native-like binding modes should be classed as having "state-of-the-art" performance. We use PoseBusters to compare five deep learning-based docking methods (DeepDock, DiffDock, EquiBind, TankBind, and Uni-Mol) and two well-established standard docking methods (AutoDock Vina and CCDC Gold) with and without an additional post-prediction energy minimisation step using a molecular mechanics force field. We show that both in terms of physical plausibility and the ability to generalise to examples that are distinct from the training data, no deep learning-based method yet outperforms classical docking tools. In addition, we find that molecular mechanics force fields contain docking-relevant physics missing from deep-learning methods. PoseBusters allows practitioners to assess docking and molecular generation methods and may inspire new inductive biases still required to improve deep learning-based methods, which will help drive the development of more accurate and more realistic predictions.

Machine-learned interatomic potentials (MLIPs) have shown significant promise in predicting infrared spectra with high fidelity. However, the absence of general-purpose MLIPs capable of handling a wide range of elements and their combinations has limited their broader applicability. In this work, we introduce MACE4IR, a machine learning foundation model built on the MACE architecture and trained on 10 million geometries and corresponding density-functional theory (DFT) energies, forces and dipole moments from the QCML dataset. The training data encompasses approximately 80 elements and a diverse set of molecules, including organic compounds, inorganic species, and metal complexes. MACE4IR accurately predicts energies, forces, dipole moments, and infrared spectra at significantly reduced computational cost compared to DFT. By combining generality, accuracy, and efficiency, MACE4IR opens the door to rapid and reliable infrared spectra prediction for complex systems across chemistry, biology, and materials science.

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries -- permutation, rotation, and translation -- for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions must be modified, and each layer must handle multiple data types for different harmonic orders. We present Facet, a GNN architecture for efficient ML potentials, developed through systematic analysis of steerable GNNs. Our innovations include replacing expensive multi-layer perceptrons (MLPs) for interatomic distances with splines, which match performance while cutting computational and memory demands. We also introduce a general-purpose equivariant layer that mixes node information via spherical grid projection followed by standard MLPs -- faster than tensor products and more expressive than linear or gate layers. On the MPTrj dataset, Facet matches leading models with far fewer parameters and under 10% of their training compute. On a crystal relaxation task, it runs twice as fast as MACE models. We further show SevenNet-0's parameters can be reduced by over 25% with no accuracy loss. These techniques enable more than 10x faster training of large-scale foundation models for ML potentials, potentially reshaping computational materials discovery.

Incorporation of machine learning (ML) techniques into atomic-scale modeling has proven to be an extremely effective strategy to improve the accuracy and reduce the computational cost of simulations. It also entails conceptual and practical challenges, as it involves combining very different mathematical foundations, as well as software ecosystems that are very well developed in their own merit, but do not share many commonalities. To address these issues and facilitate the adoption of ML in atomistic simulations, we introduce two dedicated software libraries. The first one, metatensor, provides multi-platform and multi-language storage and manipulation of arrays with many potentially sparse indices, designed from the ground up for atomistic ML applications. By combining the actual values with metadata that describes their nature and that facilitates the handling of geometric information and gradients with respect to the atomic positions, metatensor provides a common framework to enable data sharing between ML software -- typically written in Python -- and established atomistic modeling tools -- typically written in Fortran, C or C++. The second library, metatomic, provides an interface to store an atomistic ML model and metadata about this model in a portable way, facilitating the implementation, training and distribution of models, and their use across different simulation packages. We showcase a growing ecosystem of tools, from low-level libraries, training utilities, to interfaces with existing software packages that demonstrate the effectiveness of metatensor and metatomic in bridging the gap between traditional simulation software and modern ML frameworks.

Transfer learning has become crucial in computer vision tasks due to the vast availability of pre-trained deep learning models. However, selecting the optimal pre-trained model from a diverse pool for a specific downstream task remains a challenge. Existing methods for measuring the transferability of pre-trained models rely on statistical correlations between encoded static features and task labels, but they overlook the impact of underlying representation dynamics during fine-tuning, leading to unreliable results, especially for self-supervised models. In this paper, we present an insightful physics-inspired approach named PED to address these challenges. We reframe the challenge of model selection through the lens of potential energy and directly model the interaction forces that influence fine-tuning dynamics. By capturing the motion of dynamic representations to decline the potential energy within a force-driven physical model, we can acquire an enhanced and more stable observation for estimating transferability. The experimental results on 10 downstream tasks and 12 self-supervised models demonstrate that our approach can seamlessly integrate into existing ranking techniques and enhance their performances, revealing its effectiveness for the model selection task and its potential for understanding the mechanism in transfer learning. Code will be available at https://github.com/lixiaotong97/PED.

Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate change. These calculations are traditionally performed using Density Functional Theory, which is computationally very expensive. Machine learning has the potential to dramatically improve the efficiency of these calculations from days or hours to seconds. We propose the Spherical Channel Network (SCN) to model atomic energies and forces. The SCN is a graph neural network where nodes represent atoms and edges their neighboring atoms. The atom embeddings are a set of spherical functions, called spherical channels, represented using spherical harmonics. We demonstrate, that by rotating the embeddings based on the 3D edge orientation, more information may be utilized while maintaining the rotational equivariance of the messages. While equivariance is a desirable property, we find that by relaxing this constraint in both message passing and aggregation, improved accuracy may be achieved. We demonstrate state-of-the-art results on the large-scale Open Catalyst dataset in both energy and force prediction for numerous tasks and metrics.

Machine learning potentials (MLPs) trained on accurate quantum chemical data can retain the high accuracy, while inflicting little computational demands. On the downside, they need to be trained for each individual system. In recent years, a vast number of MLPs has been trained from scratch because learning additional data typically requires to train again on all data to not forget previously acquired knowledge. Additionally, most common structural descriptors of MLPs cannot represent efficiently a large number of different chemical elements. In this work, we tackle these problems by introducing element-embracing atom-centered symmetry functions (eeACSFs) which combine structural properties and element information from the periodic table. These eeACSFs are a key for our development of a lifelong machine learning potential (lMLP). Uncertainty quantification can be exploited to transgress a fixed, pre-trained MLP to arrive at a continuously adapting lMLP, because a predefined level of accuracy can be ensured. To extend the applicability of an lMLP to new systems, we apply continual learning strategies to enable autonomous and on-the-fly training on a continuous stream of new data. For the training of deep neural networks, we propose the continual resilient (CoRe) optimizer and incremental learning strategies relying on rehearsal of data, regularization of parameters, and the architecture of the model.

Computational quantum chemistry plays a critical role in drug discovery, chemical synthesis, and materials science. While first-principles methods, such as density functional theory (DFT), provide high accuracy in modeling electronic structures and predicting molecular properties, they are computationally expensive. Machine learning interatomic potentials (MLIPs) have emerged as promising surrogate models that aim to achieve DFT-level accuracy while enabling efficient large-scale atomistic simulations. The development of accurate and transferable MLIPs requires large-scale, high-quality datasets with both energy and force labels. Critically, MLIPs must generalize not only to stable geometries but also to intermediate, non-equilibrium conformations encountered during atomistic simulations. In this work, we introduce PubChemQCR, a large-scale dataset of molecular relaxation trajectories curated from the raw geometry optimization outputs of the PubChemQC project. PubChemQCR is the largest publicly available dataset of DFT-based relaxation trajectories for small organic molecules, comprising approximately 3.5 million trajectories and over 300 million molecular conformations computed at various levels of theory. Each conformation is labeled with both total energy and atomic forces, making the dataset suitable for training and evaluating MLIPs. To provide baselines for future developments, we benchmark nine representative MLIP models on the dataset. Our resources are publicly available at https://huggingface.co/divelab

Neural network (NN) potentials promise highly accurate molecular dynamics (MD) simulations within the computational complexity of classical MD force fields. However, when applied outside their training domain, NN potential predictions can be inaccurate, increasing the need for Uncertainty Quantification (UQ). Bayesian modeling provides the mathematical framework for UQ, but classical Bayesian methods based on Markov chain Monte Carlo (MCMC) are computationally intractable for NN potentials. By training graph NN potentials for coarse-grained systems of liquid water and alanine dipeptide, we demonstrate here that scalable Bayesian UQ via stochastic gradient MCMC (SG-MCMC) yields reliable uncertainty estimates for MD observables. We show that cold posteriors can reduce the required training data size and that for reliable UQ, multiple Markov chains are needed. Additionally, we find that SG-MCMC and the Deep Ensemble method achieve comparable results, despite shorter training and less hyperparameter tuning of the latter. We show that both methods can capture aleatoric and epistemic uncertainty reliably, but not systematic uncertainty, which needs to be minimized by adequate modeling to obtain accurate credible intervals for MD observables. Our results represent a step towards accurate UQ that is of vital importance for trustworthy NN potential-based MD simulations required for decision-making in practice.

Graph Neural Networks (GNNs) are the dominant architecture for molecular machine learning, particularly for molecular property prediction and machine learning interatomic potentials (MLIPs). GNNs perform message passing on predefined graphs often induced by a fixed radius cutoff or k-nearest neighbor scheme. While this design aligns with the locality present in many molecular tasks, a hard-coded graph can limit expressivity due to the fixed receptive field and slows down inference with sparse graph operations. In this work, we investigate whether pure, unmodified Transformers trained directly on Cartesian coordinatesx2013without predefined graphs or physical priorsx2013can approximate molecular energies and forces. As a starting point for our analysis, we demonstrate how to train a Transformer to competitive energy and force mean absolute errors under a matched training compute budget, relative to a state-of-the-art equivariant GNN on the OMol25 dataset. We discover that the Transformer learns physically consistent patternsx2013such as attention weights that decay inversely with interatomic distancex2013and flexibly adapts them across different molecular environments due to the absence of hard-coded biases. The use of a standard Transformer also unlocks predictable improvements with respect to scaling training resources, consistent with empirical scaling laws observed in other domains. Our results demonstrate that many favorable properties of GNNs can emerge adaptively in Transformers, challenging the necessity of hard-coded graph inductive biases and pointing toward standardized, scalable architectures for molecular modeling.

Accurate prediction of protein-ligand binding affinities is crucial in drug discovery, particularly during hit-to-lead and lead optimization phases, however, limitations in ligand force fields continue to impact prediction accuracy. In this work, we validate relative binding free energy (RBFE) accuracy using neural network potentials (NNPs) for the ligands. We utilize a novel NNP model, AceForce 1.0, based on the TensorNet architecture for small molecules that broadens the applicability to diverse drug-like compounds, including all important chemical elements and supporting charged molecules. Using established benchmarks, we show overall improved accuracy and correlation in binding affinity predictions compared with GAFF2 for molecular mechanics and ANI2-x for NNPs. Slightly less accuracy but comparable correlations with OPLS4. We also show that we can run the NNP simulations at 2 fs timestep, at least two times larger than previous NNP models, providing significant speed gains. The results show promise for further evolutions of free energy calculations using NNPs while demonstrating its practical use already with the current generation. The code and NNP model are publicly available for research use.

Machine learning (ML) models hold the promise of transforming atomic simulations by delivering quantum chemical accuracy at a fraction of the computational cost. Realization of this potential would enable high-throughout, high-accuracy molecular screening campaigns to explore vast regions of chemical space and facilitate ab initio simulations at sizes and time scales that were previously inaccessible. However, a fundamental challenge to creating ML models that perform well across molecular chemistry is the lack of comprehensive data for training. Despite substantial efforts in data generation, no large-scale molecular dataset exists that combines broad chemical diversity with a high level of accuracy. To address this gap, Meta FAIR introduces Open Molecules 2025 (OMol25), a large-scale dataset composed of more than 100 million density functional theory (DFT) calculations at the omegaB97M-V/def2-TZVPD level of theory, representing billions of CPU core-hours of compute. OMol25 uniquely blends elemental, chemical, and structural diversity including: 83 elements, a wide-range of intra- and intermolecular interactions, explicit solvation, variable charge/spin, conformers, and reactive structures. There are ~83M unique molecular systems in OMol25 covering small molecules, biomolecules, metal complexes, and electrolytes, including structures obtained from existing datasets. OMol25 also greatly expands on the size of systems typically included in DFT datasets, with systems of up to 350 atoms. In addition to the public release of the data, we provide baseline models and a comprehensive set of model evaluations to encourage community engagement in developing the next-generation ML models for molecular chemistry.

While molecular pre-training has shown great potential in enhancing drug discovery, the lack of a solid physical interpretation in current methods raises concerns about whether the learned representation truly captures the underlying explanatory factors in observed data, ultimately resulting in limited generalization and robustness. Although denoising methods offer a physical interpretation, their accuracy is often compromised by ad-hoc noise design, leading to inaccurate learned force fields. To address this limitation, this paper proposes a new method for molecular pre-training, called sliced denoising (SliDe), which is based on the classical mechanical intramolecular potential theory. SliDe utilizes a novel noise strategy that perturbs bond lengths, angles, and torsion angles to achieve better sampling over conformations. Additionally, it introduces a random slicing approach that circumvents the computationally expensive calculation of the Jacobian matrix, which is otherwise essential for estimating the force field. By aligning with physical principles, SliDe shows a 42\% improvement in the accuracy of estimated force fields compared to current state-of-the-art denoising methods, and thus outperforms traditional baselines on various molecular property prediction tasks.

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that leverages Cartesian tensor representations. By using Cartesian tensor atomic embeddings, feature mixing is simplified through matrix product operations. Furthermore, the cost-effective decomposition of these tensors into rotation group irreducible representations allows for the separate processing of scalars, vectors, and tensors when necessary. Compared to higher-rank spherical tensor models, TensorNet demonstrates state-of-the-art performance with significantly fewer parameters. For small molecule potential energies, this can be achieved even with a single interaction layer. As a result of all these properties, the model's computational cost is substantially decreased. Moreover, the accurate prediction of vector and tensor molecular quantities on top of potential energies and forces is possible. In summary, TensorNet's framework opens up a new space for the design of state-of-the-art equivariant models.

Machine learning interatomic potentials (MLIPs) have become increasingly effective at approximating quantum mechanical calculations at a fraction of the computational cost. However, lower errors on held out test sets do not always translate to improved results on downstream physical property prediction tasks. In this paper, we propose testing MLIPs on their practical ability to conserve energy during molecular dynamic simulations. If passed, improved correlations are found between test errors and their performance on physical property prediction tasks. We identify choices which may lead to models failing this test, and use these observations to improve upon highly-expressive models. The resulting model, eSEN, provides state-of-the-art results on a range of physical property prediction tasks, including materials stability prediction, thermal conductivity prediction, and phonon calculations.

Supervised machine learning approaches have been increasingly used in accelerating electronic structure prediction as surrogates of first-principle computational methods, such as density functional theory (DFT). While numerous quantum chemistry datasets focus on chemical properties and atomic forces, the ability to achieve accurate and efficient prediction of the Hamiltonian matrix is highly desired, as it is the most important and fundamental physical quantity that determines the quantum states of physical systems and chemical properties. In this work, we generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 999 or 2998 molecular dynamics trajectories and 130,831 stable molecular geometries, based on the QM9 dataset. By designing benchmark tasks with various molecules, we show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules. Both the QH9 dataset and the baseline models are provided to the community through an open-source benchmark, which can be highly valuable for developing machine learning methods and accelerating molecular and materials design for scientific and technological applications. Our benchmark is publicly available at https://github.com/divelab/AIRS/tree/main/OpenDFT/QHBench.

The dynamic nature of proteins is crucial for determining their biological functions and properties, for which Monte Carlo (MC) and molecular dynamics (MD) simulations stand as predominant tools to study such phenomena. By utilizing empirically derived force fields, MC or MD simulations explore the conformational space through numerically evolving the system via Markov chain or Newtonian mechanics. However, the high-energy barrier of the force fields can hamper the exploration of both methods by the rare event, resulting in inadequately sampled ensemble without exhaustive running. Existing learning-based approaches perform direct sampling yet heavily rely on target-specific simulation data for training, which suffers from high data acquisition cost and poor generalizability. Inspired by simulated annealing, we propose Str2Str, a novel structure-to-structure translation framework capable of zero-shot conformation sampling with roto-translation equivariant property. Our method leverages an amortized denoising score matching objective trained on general crystal structures and has no reliance on simulation data during both training and inference. Experimental results across several benchmarking protein systems demonstrate that Str2Str outperforms previous state-of-the-art generative structure prediction models and can be orders of magnitude faster compared to long MD simulations. Our open-source implementation is available at https://github.com/lujiarui/Str2Str

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

Computational catalysis is playing an increasingly significant role in the design of catalysts across a wide range of applications. A common task for many computational methods is the need to accurately compute the minimum binding energy - the adsorption energy - for an adsorbate and a catalyst surface of interest. Traditionally, the identification of low energy adsorbate-surface configurations relies on heuristic methods and researcher intuition. As the desire to perform high-throughput screening increases, it becomes challenging to use heuristics and intuition alone. In this paper, we demonstrate machine learning potentials can be leveraged to identify low energy adsorbate-surface configurations more accurately and efficiently. Our algorithm provides a spectrum of trade-offs between accuracy and efficiency, with one balanced option finding the lowest energy configuration, within a 0.1 eV threshold, 86.33% of the time, while achieving a 1331x speedup in computation. To standardize benchmarking, we introduce the Open Catalyst Dense dataset containing nearly 1,000 diverse surfaces and 85,658 unique configurations.

Methods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their applications. Neural network potentials (NNPs) are a promising alternative to quantum chemistry methods, but they require large and diverse datasets for training. This work presents a new dataset and benchmark called nabla^2DFT that is based on the nablaDFT. It contains twice as much molecular structures, three times more conformations, new data types and tasks, and state-of-the-art models. The dataset includes energies, forces, 17 molecular properties, Hamiltonian and overlap matrices, and a wavefunction object. All calculations were performed at the DFT level (omegaB97X-D/def2-SVP) for each conformation. Moreover, nabla^2DFT is the first dataset that contains relaxation trajectories for a substantial number of drug-like molecules. We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks. Finally, we propose an extendable framework for training NNPs and implement 10 models within it.

This work presents a probabilistic digital twin framework for response prediction in dynamical systems governed by misspecified physics. The approach integrates Gaussian Process Latent Force Models (GPLFM) and Bayesian Neural Networks (BNNs) to enable end-to-end uncertainty-aware inference and prediction. In the diagnosis phase, model-form errors (MFEs) are treated as latent input forces to a nominal linear dynamical system and jointly estimated with system states using GPLFM from sensor measurements. A BNN is then trained on posterior samples to learn a probabilistic nonlinear mapping from system states to MFEs, while capturing diagnostic uncertainty. For prognosis, this mapping is used to generate pseudo-measurements, enabling state prediction via Kalman filtering. The framework allows for systematic propagation of uncertainty from diagnosis to prediction, a key capability for trustworthy digital twins. The framework is demonstrated using four nonlinear examples: a single degree of freedom (DOF) oscillator, a multi-DOF system, and two established benchmarks -- the Bouc-Wen hysteretic system and the Silverbox experimental dataset -- highlighting its predictive accuracy and robustness to model misspecification.

Machine learning interatomic potentials (MLIPs) balance high accuracy and lower costs compared to density functional theory calculations, but their performance often depends on the size and diversity of training datasets. Large datasets improve model accuracy and generalization but are computationally expensive to produce and train on, while smaller datasets risk discarding rare but important atomic environments and compromising MLIP accuracy/reliability. Here, we develop an information-theoretical framework to quantify the efficiency of dataset compression methods and propose an algorithm that maximizes this efficiency. By framing atomistic dataset compression as an instance of the minimum set cover (MSC) problem over atom-centered environments, our method identifies the smallest subset of structures that contains as much information as possible from the original dataset while pruning redundant information. The approach is extensively demonstrated on the GAP-20 and TM23 datasets, and validated on 64 varied datasets from the ColabFit repository. Across all cases, MSC consistently retains outliers, preserves dataset diversity, and reproduces the long-tail distributions of forces even at high compression rates, outperforming other subsampling methods. Furthermore, MLIPs trained on MSC-compressed datasets exhibit reduced error for out-of-distribution data even in low-data regimes. We explain these results using an outlier analysis and show that such quantitative conclusions could not be achieved with conventional dimensionality reduction methods. The algorithm is implemented in the open-source QUESTS package and can be used for several tasks in atomistic modeling, from data subsampling, outlier detection, and training improved MLIPs at a lower cost.

We propose a machine learning method to model molecular tensorial quantities, namely the magnetic anisotropy tensor, based on the Gaussian-moment neural-network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3--0.4 cm^{-1} and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.

Foundation models have revolutionized natural language processing through a ``train once, deploy anywhere'' paradigm, where a single pre-trained model adapts to countless downstream tasks without retraining. Access to a Physics Foundation Model (PFM) would be transformative -- democratizing access to high-fidelity simulations, accelerating scientific discovery, and eliminating the need for specialized solver development. Yet current physics-aware machine learning approaches remain fundamentally limited to single, narrow domains and require retraining for each new system. We present the General Physics Transformer (GPhyT), trained on 1.8 TB of diverse simulation data, that demonstrates foundation model capabilities are achievable for physics. Our key insight is that transformers can learn to infer governing dynamics from context, enabling a single model to simulate fluid-solid interactions, shock waves, thermal convection, and multi-phase dynamics without being told the underlying equations. GPhyT achieves three critical breakthroughs: (1) superior performance across multiple physics domains, outperforming specialized architectures by up to 29x, (2) zero-shot generalization to entirely unseen physical systems through in-context learning, and (3) stable long-term predictions through 50-timestep rollouts. By establishing that a single model can learn generalizable physical principles from data alone, this work opens the path toward a universal PFM that could transform computational science and engineering.

The groundbreaking advance in materials and chemical research has been driven by the development of atomistic simulations. However, the broader applicability of the atomistic simulations remains restricted, as they inherently depend on energy models that are either inaccurate or computationally prohibitive. Machine learning interatomic potentials (MLIPs) have recently emerged as a promising class of energy models, but their deployment remains challenging due to the lack of systematic protocols for generating diverse training data. Here we automate the construction of training datasets to enable the development of general-purpose MLIPs, by introducing GAIA, an end-to-end framework to build a wide range of atomic arrangements. By employing systematic evaluation of metadynamics for effective structural exploration, GAIA overcomes the heuristic nature of conventional dataset generation. Using GAIA, we constructed Titan25, a benchmark-scale dataset, and trained MLIPs that closely match both static and dynamic density functional theory results. The models further reproduce experimental observations across reactive regimes, including detonation, coalescence, and catalytic activity. GAIA narrows the gap between experiment and simulation, and paves the way for the development of universal MLIPs that can reliably describe a wide spectrum of materials and chemical processes.

Accurate potential energy surface (PES) descriptions are essential for atomistic simulations of materials. Universal machine learning interatomic potentials (UMLIPs)^{1-3} offer a computationally efficient alternative to density functional theory (DFT)^4 for PES modeling across the periodic table. However, their accuracy today is fundamentally constrained due to a reliance on DFT relaxation data.^{5,6} Here, we introduce MatPES, a foundational PES dataset comprising sim 400,000 structures carefully sampled from 281 million molecular dynamics snapshots that span 16 billion atomic environments. We demonstrate that UMLIPs trained on the modestly sized MatPES dataset can rival, or even outperform, prior models trained on much larger datasets across a broad range of equilibrium, near-equilibrium, and molecular dynamics property benchmarks. We also introduce the first high-fidelity PES dataset based on the revised regularized strongly constrained and appropriately normed (r^2SCAN) functional^7 with greatly improved descriptions of interatomic bonding. The open source MatPES initiative emphasizes the importance of data quality over quantity in materials science and enables broad community-driven advancements toward more reliable, generalizable, and efficient UMLIPs for large-scale materials discovery and design.

Catalysis at solid-liquid interfaces plays a central role in the advancement of energy storage and sustainable chemical production technologies. By enabling accurate, long-time scale simulations, machine learning (ML) models have the potential to accelerate the discovery of (electro)catalysts. While prior Open Catalyst datasets (OC20 and OC22) have advanced the field by providing large-scale density functional theory (DFT) data of adsorbates on surfaces at solid-gas interfaces, they do not capture the critical role of solvent and electrolyte effects at solid-liquid interfaces. To bridge this gap, we introduce the Open Catalyst 2025 (OC25) dataset, consisting of 7,801,261 calculations across 1,511,270 unique explicit solvent environments. OC25 constitutes the largest and most diverse solid-liquid interface dataset that is currently available and provides configurational and elemental diversity: spanning 88 elements, commonly used solvents/ions, varying solvent layers, and off-equilibrium sampling. State-of-the-art models trained on the OC25 dataset exhibit energy, force, and solvation energy errors as low as 0.1 eV, 0.015 eV/A, and 0.04 eV, respectively; significantly lower than than the recently released Universal Models for Atoms (UMA-OC20). Additionally, we discuss the impact of the quality of DFT-calculated forces on model training and performance. The dataset and accompanying baseline models are made openly available for the community. We anticipate the dataset to facilitate large length-scale and long-timescale simulations of catalytic transformations at solid-liquid interfaces, advancing molecular-level insights into functional interfaces and enabling the discovery of next-generation energy storage and conversion technologies.

In this paper we tackle the problem of generating conformers of a molecule in 3D space given its molecular graph. We parameterize these conformers as continuous functions that map elements from the molecular graph to points in 3D space. We then formulate the problem of learning to generate conformers as learning a distribution over these functions using a diffusion generative model, called Molecular Conformer Fields (MCF). Our approach is simple and scalable, and achieves state-of-the-art performance on challenging molecular conformer generation benchmarks while making no assumptions about the explicit structure of molecules (e.g. modeling torsional angles). MCF represents an advance in extending diffusion models to handle complex scientific problems in a conceptually simple, scalable and effective manner.

Accurate prediction of atomistic, thermodynamic, and kinetic properties from molecular structures underpins materials innovation. Existing computational and experimental approaches lack the scalability required to efficiently navigate chemical space. Scientific foundation models trained on large unlabeled datasets offer a path toward exploring chemical space across diverse application domains. Here we develop MIST, a family of molecular foundation models with up to an order of magnitude more parameters and data than prior works. Trained using a novel tokenization scheme that comprehensively captures nuclear, electronic, and geometric information, MIST learns from a diverse range of molecules. MIST models have been fine-tuned to predict more than 400 structure -- property relationships and match or exceed state-of-the-art performance across benchmarks spanning physiology, electrochemistry, and quantum chemistry. We demonstrate the ability of these models to solve real-world problems across chemical space, including multiobjective electrolyte solvent screening, olfactory perception mapping, isotope half-life prediction, stereochemical reasoning for chiral organometallic compounds, and binary and multi-component mixture property prediction. Probing MIST models using mechanistic interpretability methods reveals identifiable patterns and trends not explicitly present in the training data, suggesting that the models learn generalizable scientific concepts. We formulate hyperparameter-penalized Bayesian neural scaling laws and use them to reduce the computational cost of model development by an order of magnitude. The methods and findings presented here represent a significant step toward accelerating materials discovery, design, and optimization using foundation models and provide valuable guidance for training compute-optimal scientific foundation models.

A number of recent self-supervised learning methods have shown impressive performance on image classification and other tasks. A somewhat bewildering variety of techniques have been used, not always with a clear understanding of the reasons for their benefits, especially when used in combination. Here we treat the embeddings of images as point particles and consider model optimization as a dynamic process on this system of particles. Our dynamic model combines an attractive force for similar images, a locally dispersive force to avoid local collapse, and a global dispersive force to achieve a globally-homogeneous distribution of particles. The dynamic perspective highlights the advantage of using a delayed-parameter image embedding (a la BYOL) together with multiple views of the same image. It also uses a purely-dynamic local dispersive force (Brownian motion) that shows improved performance over other methods and does not require knowledge of other particle coordinates. The method is called MSBReg which stands for (i) a Multiview centroid loss, which applies an attractive force to pull different image view embeddings toward their centroid, (ii) a Singular value loss, which pushes the particle system toward spatially homogeneous density, (iii) a Brownian diffusive loss. We evaluate downstream classification performance of MSBReg on ImageNet as well as transfer learning tasks including fine-grained classification, multi-class object classification, object detection, and instance segmentation. In addition, we also show that applying our regularization term to other methods further improves their performance and stabilize the training by preventing a mode collapse.

We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. We find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network. We then apply our method to a non-trivial cosmology example-a detailed dark matter simulation-and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

Machine learning-based surrogate models have emerged as a powerful tool to accelerate simulation-driven scientific workflows. However, their widespread adoption is hindered by the lack of large-scale, diverse, and standardized datasets tailored to physics-based simulations. While existing initiatives provide valuable contributions, many are limited in scope-focusing on specific physics domains, relying on fragmented tooling, or adhering to overly simplistic datamodels that restrict generalization. To address these limitations, we introduce PLAID (Physics-Learning AI Datamodel), a flexible and extensible framework for representing and sharing datasets of physics simulations. PLAID defines a unified standard for describing simulation data and is accompanied by a library for creating, reading, and manipulating complex datasets across a wide range of physical use cases (gitlab.com/drti/plaid). We release six carefully crafted datasets under the PLAID standard, covering structural mechanics and computational fluid dynamics, and provide baseline benchmarks using representative learning methods. Benchmarking tools are made available on Hugging Face, enabling direct participation by the community and contribution to ongoing evaluation efforts (huggingface.co/PLAIDcompetitions).

Knowledge of mixtures' phase equilibria is crucial in nature and technical chemistry. Phase equilibria calculations of mixtures require activity coefficients. However, experimental data on activity coefficients is often limited due to high cost of experiments. For an accurate and efficient prediction of activity coefficients, machine learning approaches have been recently developed. However, current machine learning approaches still extrapolate poorly for activity coefficients of unknown molecules. In this work, we introduce the SMILES-to-Properties-Transformer (SPT), a natural language processing network to predict binary limiting activity coefficients from SMILES codes. To overcome the limitations of available experimental data, we initially train our network on a large dataset of synthetic data sampled from COSMO-RS (10 Million data points) and then fine-tune the model on experimental data (20 870 data points). This training strategy enables SPT to accurately predict limiting activity coefficients even for unknown molecules, cutting the mean prediction error in half compared to state-of-the-art models for activity coefficient predictions such as COSMO-RS, UNIFAC, and improving on recent machine learning approaches.

A longstanding goal in computer vision is to model motions from videos, while the representations behind motions, i.e. the invisible physical interactions that cause objects to deform and move, remain largely unexplored. In this paper, we study how to recover the invisible forces from visual observations, e.g., estimating the wind field by observing a leaf falling to the ground. Our key innovation is an end-to-end differentiable inverse graphics framework, which jointly models object geometry, physical properties, and interactions directly from videos. Through backpropagation, our approach enables the recovery of force representations from object motions. We validate our method on both synthetic and real-world scenarios, and the results demonstrate its ability to infer plausible force fields from videos. Furthermore, we show the potential applications of our approach, including physics-based video generation and editing. We hope our approach sheds light on understanding and modeling the physical process behind pixels, bridging the gap between vision and physics. Please check more video results in our https://chaoren2357.github.io/seeingthewind/{project page}.

Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric retrieval by implementing a random forest to perform retrievals in seconds that are consistent with the traditional, computationally-expensive nested-sampling retrieval method. We expand upon their approach by presenting a new machine learning model, plan-net, based on an ensemble of Bayesian neural networks that yields more accurate inferences than the random forest for the same data set of synthetic transmission spectra. We demonstrate that an ensemble provides greater accuracy and more robust uncertainties than a single model. In addition to being the first to use Bayesian neural networks for atmospheric retrieval, we also introduce a new loss function for Bayesian neural networks that learns correlations between the model outputs. Importantly, we show that designing machine learning models to explicitly incorporate domain-specific knowledge both improves performance and provides additional insight by inferring the covariance of the retrieved atmospheric parameters. We apply plan-net to the Hubble Space Telescope Wide Field Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal temperature and water abundance consistent with the literature. We highlight that our method is flexible and can be expanded to higher-resolution spectra and a larger number of atmospheric parameters.

Recently, pre-trained foundation models have enabled significant advancements in multiple fields. In molecular machine learning, however, where datasets are often hand-curated, and hence typically small, the lack of datasets with labeled features, and codebases to manage those datasets, has hindered the development of foundation models. In this work, we present seven novel datasets categorized by size into three distinct categories: ToyMix, LargeMix and UltraLarge. These datasets push the boundaries in both the scale and the diversity of supervised labels for molecular learning. They cover nearly 100 million molecules and over 3000 sparsely defined tasks, totaling more than 13 billion individual labels of both quantum and biological nature. In comparison, our datasets contain 300 times more data points than the widely used OGB-LSC PCQM4Mv2 dataset, and 13 times more than the quantum-only QM1B dataset. In addition, to support the development of foundational models based on our proposed datasets, we present the Graphium graph machine learning library which simplifies the process of building and training molecular machine learning models for multi-task and multi-level molecular datasets. Finally, we present a range of baseline results as a starting point of multi-task and multi-level training on these datasets. Empirically, we observe that performance on low-resource biological datasets show improvement by also training on large amounts of quantum data. This indicates that there may be potential in multi-task and multi-level training of a foundation model and fine-tuning it to resource-constrained downstream tasks.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

We explore the integration of Kolmogorov Networks (KANs) into molecular dynamics (MD) simulations to improve interatomic potentials. We propose that widely used potentials, such as the Lennard-Jones (LJ) potential, the embedded atom model (EAM), and artificial neural network (ANN) potentials, can be interpreted within the KAN framework. Specifically, we demonstrate that the descriptors for ANN potentials, typically constructed using polynomials, can be redefined using KAN's non-linear functions. By employing linear or cubic spline interpolations for these KAN functions, we show that the computational cost of evaluating ANN potentials and their derivatives is reduced.

Foundation models have achieved remarkable success across video, image, and language domains. By scaling up the number of parameters and training datasets, these models acquire generalizable world knowledge and often surpass task-specific approaches. However, such progress has yet to extend to the domain of physics simulation. A primary bottleneck is data scarcity: while millions of images, videos, and textual resources are readily available on the internet, the largest physics simulation datasets contain only tens of thousands of samples. This data limitation hinders the use of large models, as overfitting becomes a major concern. As a result, physics applications typically rely on small models, which struggle with long-range prediction due to limited context understanding. Additionally, unlike images, videos, or text-which typically exhibit fixed granularity-physics datasets often vary drastically in scale, amplifying the challenges of scaling up multitask training. We introduce PhysiX, the first large-scale foundation model for physics simulation. PhysiX is a 4.5B parameter autoregressive generative model. It uses a discrete tokenizer to encode physical processes at different scales into a sequence of discrete tokens, and employs an autoregressive next-token prediction objective to model such processes in the token space. To mitigate the rounding error in the discretization process, PhysiX incorporates a specialized refinement module. Through extensive experiments, we show that PhysiX effectively addresses the data bottleneck, outperforming task-specific baselines under comparable settings as well as the previous absolute state-of-the-art approaches on The Well benchmark. Our results indicate that knowledge learned from natural videos can be successfully transferred to physics simulation, and that joint training across diverse simulation tasks enables synergistic learning.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

Large Language Models (LLMs) have achieved remarkable progress on advanced reasoning tasks such as mathematics and coding competitions. Meanwhile, physics, despite being both reasoning-intensive and essential to real-world understanding, received limited academic and industrial attention. This paper introduces PHYSICS, a dataset containing 16,568 high-quality physics problems spanning subjects and difficulty levels, to facilitate this issue. Specifically, PHYSICS is curated with exercises from over 100 textbooks through a carefully designed pipeline for quality control. It covers five major physics domains: Mechanics, Electromagnetism, Thermodynamics, Optics, and Modern Physics. It also spans a wide range of difficulty levels, from high school to graduate-level physics courses. To utilize the data for improving and evaluating the model's physical reasoning capabilities, we split the dataset into training and test sets, and provide reasoning paths generated by powerful reasoning models for the training data to facilitate model training. In addition, for the evaluation part, we find that existing evaluation frameworks exhibit biases in aspects such as units, simplification, and precision in physics domain. To balance efficiency and accuracy, we introduce a Rule+Model evaluation framework tailored to physics problems. Our evaluations on current state-of-the-art open-source and proprietary models highlight the limitations of current models in handling physics-related tasks. We hope that our dataset and evaluation methodology will jointly advance the development of LLMs in the field of physics.

Solving mechanics problems using numerical methods requires comprehensive intelligent capability of retrieving relevant knowledge and theory, constructing and executing codes, analyzing the results, a task that has thus far mainly been reserved for humans. While emerging AI methods can provide effective approaches to solve end-to-end problems, for instance via the use of deep surrogate models or various data analytics strategies, they often lack physical intuition since knowledge is baked into the parametric complement through training, offering less flexibility when it comes to incorporating mathematical or physical insights. By leveraging diverse capabilities of multiple dynamically interacting large language models (LLMs), we can overcome the limitations of conventional approaches and develop a new class of physics-inspired generative machine learning platform, here referred to as MechAgents. A set of AI agents can solve mechanics tasks, here demonstrated for elasticity problems, via autonomous collaborations. A two-agent team can effectively write, execute and self-correct code, in order to apply finite element methods to solve classical elasticity problems in various flavors (different boundary conditions, domain geometries, meshes, small/finite deformation and linear/hyper-elastic constitutive laws, and others). For more complex tasks, we construct a larger group of agents with enhanced division of labor among planning, formulating, coding, executing and criticizing the process and results. The agents mutually correct each other to improve the overall team-work performance in understanding, formulating and validating the solution. Our framework shows the potential of synergizing the intelligence of language models, the reliability of physics-based modeling, and the dynamic collaborations among diverse agents, opening novel avenues for automation of solving engineering problems.

A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold Networks (KANs) and science. The framework highlights KANs' usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in the pykan package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN compiler that compiles symbolic formulas into KANs. (3) tree converter: convert KANs (or any neural networks) to tree graphs. Based on these tools, we demonstrate KANs' capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.

Ligand strain energy, the energy difference between the bound and unbound conformations of a ligand, is an important component of structure-based small molecule drug design. A large majority of observed ligands in protein-small molecule co-crystal structures bind in low-strain conformations, making strain energy a useful filter for structure-based drug design. In this work we present a tool for calculating ligand strain with a high accuracy. StrainRelief uses a MACE Neural Network Potential (NNP), trained on a large database of Density Functional Theory (DFT) calculations to estimate ligand strain of neutral molecules with quantum accuracy. We show that this tool estimates strain energy differences relative to DFT to within 1.4 kcal/mol, more accurately than alternative NNPs. These results highlight the utility of NNPs in drug discovery, and provide a useful tool for drug discovery teams.

We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as the quality and quantity of the training dataset and the network storage, valid in the limit of large network size and structureless datasets. Moreover, we establish a bridge between macroscopic observables standardly used in statistical mechanics and loss functions typically used in the machine learning. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate neural networks in general.

Molecular conformation optimization is crucial to computer-aided drug discovery and materials design. Traditional energy minimization techniques rely on iterative optimization methods that use molecular forces calculated by a physical simulator (oracle) as anti-gradients. However, this is a computationally expensive approach that requires many interactions with a physical simulator. One way to accelerate this procedure is to replace the physical simulator with a neural network. Despite recent progress in neural networks for molecular conformation energy prediction, such models are prone to distribution shift, leading to inaccurate energy minimization. We find that the quality of energy minimization with neural networks can be improved by providing optimization trajectories as additional training data. Still, it takes around 5 times 10^5 additional conformations to match the physical simulator's optimization quality. In this work, we present the Gradual Optimization Learning Framework (GOLF) for energy minimization with neural networks that significantly reduces the required additional data. The framework consists of an efficient data-collecting scheme and an external optimizer. The external optimizer utilizes gradients from the energy prediction model to generate optimization trajectories, and the data-collecting scheme selects additional training data to be processed by the physical simulator. Our results demonstrate that the neural network trained with GOLF performs on par with the oracle on a benchmark of diverse drug-like molecules using 50x less additional data.

Molecular machine learning has been maturing rapidly over the last few years. Improved methods and the presence of larger datasets have enabled machine learning algorithms to make increasingly accurate predictions about molecular properties. However, algorithmic progress has been limited due to the lack of a standard benchmark to compare the efficacy of proposed methods; most new algorithms are benchmarked on different datasets making it challenging to gauge the quality of proposed methods. This work introduces MoleculeNet, a large scale benchmark for molecular machine learning. MoleculeNet curates multiple public datasets, establishes metrics for evaluation, and offers high quality open-source implementations of multiple previously proposed molecular featurization and learning algorithms (released as part of the DeepChem open source library). MoleculeNet benchmarks demonstrate that learnable representations are powerful tools for molecular machine learning and broadly offer the best performance. However, this result comes with caveats. Learnable representations still struggle to deal with complex tasks under data scarcity and highly imbalanced classification. For quantum mechanical and biophysical datasets, the use of physics-aware featurizations can be more important than choice of particular learning algorithm.

Machine learning has promised to change the landscape of laboratory chemistry, with impressive results in molecular property prediction and reaction retro-synthesis. However, chemical datasets are often inaccessible to the machine learning community as they tend to require cleaning, thorough understanding of the chemistry, or are simply not available. In this paper, we introduce a novel dataset for yield prediction, providing the first-ever transient flow dataset for machine learning benchmarking, covering over 1200 process conditions. While previous datasets focus on discrete parameters, our experimental set-up allow us to sample a large number of continuous process conditions, generating new challenges for machine learning models. We focus on solvent selection, a task that is particularly difficult to model theoretically and therefore ripe for machine learning applications. We showcase benchmarking for regression algorithms, transfer-learning approaches, feature engineering, and active learning, with important applications towards solvent replacement and sustainable manufacturing.

Large-scale datasets have enabled highly accurate machine learning interatomic potentials (MLIPs) for general-purpose heterogeneous catalysis modeling. There are, however, some limitations in what can be treated with these potentials because of gaps in the underlying training data. To extend these capabilities, we introduce AQCat25, a complementary dataset of 13.5 million density functional theory (DFT) single point calculations designed to improve the treatment of systems where spin polarization and/or higher fidelity are critical. We also investigate methodologies for integrating new datasets, such as AQCat25, with the broader Open Catalyst 2020 (OC20) dataset to create spin-aware models without sacrificing generalizability. We find that directly tuning a general model on AQCat25 leads to catastrophic forgetting of the original dataset's knowledge. Conversely, joint training strategies prove effective for improving accuracy on the new data without sacrificing general performance. This joint approach introduces a challenge, as the model must learn from a dataset containing both mixed-fidelity calculations and mixed-physics (spin-polarized vs. unpolarized). We show that explicitly conditioning the model on this system-specific metadata, for example by using Feature-wise Linear Modulation (FiLM), successfully addresses this challenge and further enhances model accuracy. Ultimately, our work establishes an effective protocol for bridging DFT fidelity domains to advance the predictive power of foundational models in catalysis.

We report a flexible multi-modal mechanics language model, MeLM, applied to solve various nonlinear forward and inverse problems, that can deal with a set of instructions, numbers and microstructure data. The framework is applied to various examples including bio-inspired hierarchical honeycomb design, carbon nanotube mechanics, and protein unfolding. In spite of the flexible nature of the model-which allows us to easily incorporate diverse materials, scales, and mechanical features-it performs well across disparate forward and inverse tasks. Based on an autoregressive attention-model, MeLM effectively represents a large multi-particle system consisting of hundreds of millions of neurons, where the interaction potentials are discovered through graph-forming self-attention mechanisms that are then used to identify relationships from emergent structures, while taking advantage of synergies discovered in the training data. We show that the model can solve complex degenerate mechanics design problems and determine novel material architectures across a range of hierarchical levels, providing an avenue for materials discovery and analysis. Looking beyond the demonstrations reported in this paper, we discuss other opportunities in applied mechanics and general considerations about the use of large language models in modeling, design, and analysis that can span a broad spectrum of material properties from mechanical, thermal, optical, to electronic.

Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the system domain, where the type of system remains consistent and thus cannot ensure the adaptation to new, or unseen physical systems governed by different laws. For instance, a neural network trained on a mass-spring system cannot guarantee accurate predictions for the behavior of a two-body system or any other system with different physical laws. In this work, we take a significant leap forward by targeting cross domain generalization within the field of Hamiltonian dynamics. We model our system with a graph neural network and employ a meta learning algorithm to enable the model to gain experience over a distribution of tasks and make it adapt to new physics. Our approach aims to learn a unified Hamiltonian representation that is generalizable across multiple system domains, thereby overcoming the limitations of system-specific models. Our results demonstrate that the meta-trained model not only adapts effectively to new systems but also captures a generalized Hamiltonian representation that is consistent across different physical domains. Overall, through the use of meta learning, we offer a framework that achieves cross domain generalization, providing a step towards a unified model for understanding a wide array of dynamical systems via deep learning.

Recent advances in video generation models have sparked interest in world models capable of simulating realistic environments. While navigation has been well-explored, physically meaningful interactions that mimic real-world forces remain largely understudied. In this work, we investigate using physical forces as a control signal for video generation and propose force prompts which enable users to interact with images through both localized point forces, such as poking a plant, and global wind force fields, such as wind blowing on fabric. We demonstrate that these force prompts can enable videos to respond realistically to physical control signals by leveraging the visual and motion prior in the original pretrained model, without using any 3D asset or physics simulator at inference. The primary challenge of force prompting is the difficulty in obtaining high quality paired force-video training data, both in the real world due to the difficulty of obtaining force signals, and in synthetic data due to limitations in the visual quality and domain diversity of physics simulators. Our key finding is that video generation models can generalize remarkably well when adapted to follow physical force conditioning from videos synthesized by Blender, even with limited demonstrations of few objects. Our method can generate videos which simulate forces across diverse geometries, settings, and materials. We also try to understand the source of this generalization and perform ablations that reveal two key elements: visual diversity and the use of specific text keywords during training. Our approach is trained on only around 15k training examples for a single day on four A100 GPUs, and outperforms existing methods on force adherence and physics realism, bringing world models closer to real-world physics interactions. We release all datasets, code, weights, and interactive video demos at our project page.

Classification algorithms have recently found applications in computational physics for the selection of numerical methods or models adapted to the environment and the state of the physical system. For such classification tasks, labeled training data come from numerical simulations and generally correspond to physical fields discretized on a mesh. Three challenging difficulties arise: the lack of training data, their high dimensionality, and the non-applicability of common data augmentation techniques to physics data. This article introduces two algorithms to address these issues, one for dimensionality reduction via feature selection, and one for data augmentation. These algorithms are combined with a wide variety of classifiers for their evaluation. When combined with a stacking ensemble made of six multilayer perceptrons and a ridge logistic regression, they enable reaching an accuracy of 90% on our classification problem for nonlinear structural mechanics.

Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) show considerable potential in their capacity to identify solutions to complex differential equations. Over the past two years, much work has gone into the development of PINNs capable of solving the gravity field modeling problem -- i.e.\ learning a differentiable form of the gravitational potential from position and acceleration estimates. While the past PINN gravity models (PINN-GMs) have demonstrated advantages in model compactness, robustness to noise, and sample efficiency; there remain key modeling challenges which this paper aims to address. Specifically, this paper introduces the third generation of the Physics-Informed Neural Network Gravity Model (PINN-GM-III) which solves the problems of extrapolation error, bias towards low-altitude samples, numerical instability at high-altitudes, and compliant boundary conditions through numerous modifications to the model's design. The PINN-GM-III is tested by modeling a known heterogeneous density asteroid, and its performance is evaluated using seven core metrics which showcases its strengths against its predecessors and other analytic and numerical gravity models.

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach to solve physics-based initial value problems using unsupervised machine learning. We propose a deep learning framework that models the dynamics of a variety of mechanical systems through neural networks. Our framework is flexible, allowing us to solve non-linear, coupled, and chaotic dynamical systems. We demonstrate the effectiveness of our approach on systems including a free particle, a particle in a gravitational field, a classical pendulum, and the H\'enon--Heiles system (a pair of coupled harmonic oscillators with a non-linear perturbation, used in celestial mechanics). Our results show that deep neural networks can successfully approximate solutions to these problems, producing trajectories which conserve physical properties such as energy and those with stationary action. We note that probabilistic activation functions, as defined in this paper, are required to learn any solutions of initial value problems in their strictest sense, and we introduce coupled neural networks to learn solutions of coupled systems.

We introduce a novel dataset designed to benchmark the physical and spatial reasoning capabilities of Large Language Models (LLM) based on topology optimization, a method for computing optimal material distributions within a design space under prescribed loads and supports. In this dataset, LLMs are provided with conditions such as 2D boundary, applied forces and supports, and must reason about the resulting optimal material distribution. The dataset includes a variety of tasks, ranging from filling in masked regions within partial structures to predicting complete material distributions. Solving these tasks requires understanding the flow of forces and the required material distribution under given constraints, without access to simulation tools or explicit physical models, challenging models to reason about structural stability and spatial organization. Our dataset targets the evaluation of spatial and physical reasoning abilities in 2D settings, offering a complementary perspective to traditional language and logic benchmarks.

The rapid development of universal machine learning interatomic potentials (uMLIPs) has demonstrated the possibility for generalizable learning of the universal potential energy surface. In principle, the accuracy of uMLIPs can be further improved by bridging the model from lower-fidelity datasets to high-fidelity ones. In this work, we analyze the challenge of this transfer learning problem within the CHGNet framework. We show that significant energy scale shifts and poor correlations between GGA and r^2SCAN pose challenges to cross-functional data transferability in uMLIPs. By benchmarking different transfer learning approaches on the MP-r^2SCAN dataset of 0.24 million structures, we demonstrate the importance of elemental energy referencing in the transfer learning of uMLIPs. By comparing the scaling law with and without the pre-training on a low-fidelity dataset, we show that significant data efficiency can still be achieved through transfer learning, even with a target dataset of sub-million structures. We highlight the importance of proper transfer learning and multi-fidelity learning in creating next-generation uMLIPs on high-fidelity data.

Coarse-graining (CG) accelerates molecular simulations of protein dynamics by simulating sets of atoms as singular beads. Backmapping is the opposite operation of bringing lost atomistic details back from the CG representation. While machine learning (ML) has produced accurate and efficient CG simulations of proteins, fast and reliable backmapping remains a challenge. Rule-based methods produce poor all-atom geometries, needing computationally costly refinement through additional simulations. Recently proposed ML approaches outperform traditional baselines but are not transferable between proteins and sometimes generate unphysical atom placements with steric clashes and implausible torsion angles. This work addresses both issues to build a fast, transferable, and reliable generative backmapping tool for CG protein representations. We achieve generalization and reliability through a combined set of innovations: representation based on internal coordinates; an equivariant encoder/prior; a custom loss function that helps ensure local structure, global structure, and physical constraints; and expert curation of high-quality out-of-equilibrium protein data for training. Our results pave the way for out-of-the-box backmapping of coarse-grained simulations for arbitrary proteins.

In order to make accurate predictions of material properties, current machine-learning approaches generally require large amounts of data, which are often not available in practice. In this work, an all-round framework is presented which relies on a feedforward neural network, the selection of physically-meaningful features and, when applicable, joint-learning. Next to being faster in terms of training time, this approach is shown to outperform current graph-network models on small datasets. In particular, the vibrational entropy at 305 K of crystals is predicted with a mean absolute test error of 0.009 meV/K/atom (four times lower than previous studies). Furthermore, joint-learning reduces the test error compared to single-target learning and enables the prediction of multiple properties at once, such as temperature functions. Finally, the selection algorithm highlights the most important features and thus helps understanding the underlying physics.

In recent years, groundbreaking advancements in natural language processing have culminated in the emergence of powerful large language models (LLMs), which have showcased remarkable capabilities across a vast array of domains, including the understanding, generation, and translation of natural language, and even tasks that extend beyond language processing. In this report, we delve into the performance of LLMs within the context of scientific discovery, focusing on GPT-4, the state-of-the-art language model. Our investigation spans a diverse range of scientific areas encompassing drug discovery, biology, computational chemistry (density functional theory (DFT) and molecular dynamics (MD)), materials design, and partial differential equations (PDE). Evaluating GPT-4 on scientific tasks is crucial for uncovering its potential across various research domains, validating its domain-specific expertise, accelerating scientific progress, optimizing resource allocation, guiding future model development, and fostering interdisciplinary research. Our exploration methodology primarily consists of expert-driven case assessments, which offer qualitative insights into the model's comprehension of intricate scientific concepts and relationships, and occasionally benchmark testing, which quantitatively evaluates the model's capacity to solve well-defined domain-specific problems. Our preliminary exploration indicates that GPT-4 exhibits promising potential for a variety of scientific applications, demonstrating its aptitude for handling complex problem-solving and knowledge integration tasks. Broadly speaking, we evaluate GPT-4's knowledge base, scientific understanding, scientific numerical calculation abilities, and various scientific prediction capabilities.

Machine learning models, such as neural networks, decision trees, random forests, and gradient boosting machines, accept a feature vector, and provide a prediction. These models learn in a supervised fashion where we provide feature vectors mapped to the expected output. It is common practice to engineer new features from the provided feature set. Such engineered features will either augment or replace portions of the existing feature vector. These engineered features are essentially calculated fields based on the values of the other features. Engineering such features is primarily a manual, time-consuming task. Additionally, each type of model will respond differently to different kinds of engineered features. This paper reports empirical research to demonstrate what kinds of engineered features are best suited to various machine learning model types. We provide this recommendation by generating several datasets that we designed to benefit from a particular type of engineered feature. The experiment demonstrates to what degree the machine learning model can synthesize the needed feature on its own. If a model can synthesize a planned feature, it is not necessary to provide that feature. The research demonstrated that the studied models do indeed perform differently with various types of engineered features.

Large Language Models have recently gained significant attention in scientific discovery for their extensive knowledge and advanced reasoning capabilities. However, they encounter challenges in effectively simulating observational feedback and grounding it with language to propel advancements in physical scientific discovery. Conversely, human scientists undertake scientific discovery by formulating hypotheses, conducting experiments, and revising theories through observational analysis. Inspired by this, we propose to enhance the knowledge-driven, abstract reasoning abilities of LLMs with the computational strength of simulations. We introduce Scientific Generative Agent (SGA), a bilevel optimization framework: LLMs act as knowledgeable and versatile thinkers, proposing scientific hypotheses and reason about discrete components, such as physics equations or molecule structures; meanwhile, simulations function as experimental platforms, providing observational feedback and optimizing via differentiability for continuous parts, such as physical parameters. We conduct extensive experiments to demonstrate our framework's efficacy in constitutive law discovery and molecular design, unveiling novel solutions that differ from conventional human expectations yet remain coherent upon analysis.

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks. While these methods offer theoretical guarantees, they face two key limitations: (i) they primarily model local relations between adjacent time steps, overlooking longer-range or higher-level physical interactions, and (ii) they focus on forward simulation while neglecting broader physical reasoning tasks. We propose the Denoising Hamiltonian Network (DHN), a novel framework that generalizes Hamiltonian mechanics operators into more flexible neural operators. DHN captures non-local temporal relationships and mitigates numerical integration errors through a denoising mechanism. DHN also supports multi-system modeling with a global conditioning mechanism. We demonstrate its effectiveness and flexibility across three diverse physical reasoning tasks with distinct inputs and outputs.

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering and mathematical problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, and more. While this has led to solving many complex phenomena, there are some limitations. Conventional approaches such as Finite Element Methods (FEMs) and Finite Differential Methods (FDMs) require considerable time and are computationally expensive. In contrast, data driven machine learning-based methods such as neural networks provide a faster, fairly accurate alternative, and have certain advantages such as discretization invariance and resolution invariance. This article aims to provide a comprehensive insight into how data-driven approaches can complement conventional techniques to solve engineering and physics problems, while also noting some of the major pitfalls of machine learning-based approaches. Furthermore, we highlight, a novel and fast machine learning-based approach (~1000x) to learning the solution operator of a PDE operator learning. We will note how these new computational approaches can bring immense advantages in tackling many problems in fundamental and applied physics.

Obtaining the desired effect of drugs is highly dependent on their molecular geometries. Thus, the current prevailing paradigm focuses on 3D point-cloud atom representations, utilizing graph neural network (GNN) parametrizations, with rotational symmetries baked in via E(3) invariant layers. We prove that such models must necessarily disregard chirality, a geometric property of the molecules that cannot be superimposed on their mirror image by rotation and translation. Chirality plays a key role in determining drug safety and potency. To address this glaring issue, we introduce a novel field-based representation, proposing reference rotations that replace rotational symmetry constraints. The proposed model captures all molecular geometries including chirality, while still achieving highly competitive performance with E(3)-based methods across standard benchmarking metrics.

Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when dealing with strongly correlated systems. To address these shortcomings, recent work has begun to explore how machine learning can expand the capabilities of DFT; an endeavor with many open questions and technical challenges. In this work, we present Grad DFT: a fully differentiable JAX-based DFT library, enabling quick prototyping and experimentation with machine learning-enhanced exchange-correlation energy functionals. Grad DFT employs a pioneering parametrization of exchange-correlation functionals constructed using a weighted sum of energy densities, where the weights are determined using neural networks. Moreover, Grad DFT encompasses a comprehensive suite of auxiliary functions, notably featuring a just-in-time compilable and fully differentiable self-consistent iterative procedure. To support training and benchmarking efforts, we additionally compile a curated dataset of experimental dissociation energies of dimers, half of which contain transition metal atoms characterized by strong electronic correlations. The software library is tested against experimental results to study the generalization capabilities of a neural functional across potential energy surfaces and atomic species, as well as the effect of training data noise on the resulting model accuracy.

The recent advances in neural language models have also been successfully applied to the field of chemistry, offering generative solutions for classical problems in molecular design and synthesis planning. These new methods have the potential to optimize laboratory operations and fuel a new era of data-driven automation in scientific discovery. However, specialized models are still typically required for each task, leading to the need for problem-specific fine-tuning and neglecting task interrelations. The main obstacle in this field is the lack of a unified representation between natural language and chemical representations, complicating and limiting human-machine interaction. Here, we propose a multi-domain, multi-task language model to solve a wide range of tasks in both the chemical and natural language domains. By leveraging multi-task learning, our model can handle chemical and natural language concurrently, without requiring expensive pre-training on single domains or task-specific models. Interestingly, sharing weights across domains remarkably improves our model when benchmarked against state-of-the-art baselines on single-domain and cross-domain tasks. In particular, sharing information across domains and tasks gives rise to large improvements in cross-domain tasks, the magnitude of which increase with scale, as measured by more than a dozen of relevant metrics. Our work suggests that such models can robustly and efficiently accelerate discovery in physical sciences by superseding problem-specific fine-tuning and enhancing human-model interactions.

Efficient and accurate prediction of material properties is critical for advancing materials design and applications. The rapid-evolution of large language models (LLMs) presents a new opportunity for material property predictions, complementing experimental measurements and multi-scale computational methods. We focus on predicting the elastic constant tensor, as a case study, and develop domain-specific LLMs for predicting elastic constants and for materials discovery. The proposed ElaTBot LLM enables simultaneous prediction of elastic constant tensors, bulk modulus at finite temperatures, and the generation of new materials with targeted properties. Moreover, the capabilities of ElaTBot are further enhanced by integrating with general LLMs (GPT-4o) and Retrieval-Augmented Generation (RAG) for prediction. A specialized variant, ElaTBot-DFT, designed for 0 K elastic constant tensor prediction, reduces the prediction errors by 33.1% compared with domain-specific, material science LLMs (Darwin) trained on the same dataset. This natural language-based approach lowers the barriers to computational materials science and highlights the broader potential of LLMs for material property predictions and inverse design.

Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an atomistic model for glass-forming liquids. This is a notoriously difficult task, as it amounts to ergodically exploring the complex free energy landscape of a disordered and frustrated many-body system. We optimize a normalizing flow model to successfully transform high-temperature configurations of a dense liquid into low-temperature ones, near the glass transition. We perform a detailed comparative analysis with established enhanced sampling techniques developed in the physics literature to assess and rank the performance of normalizing flows against state-of-the-art algorithms. We demonstrate that machine learning methods are very promising, showing a large speedup over conventional molecular dynamics. Normalizing flows show performances comparable to parallel tempering and population annealing, while still falling far behind the swap Monte Carlo algorithm. Our study highlights the potential of generative machine learning models in scientific computing for complex systems, but also points to some of its current limitations and the need for further improvement.

Neural Fields have emerged as a transformative approach for 3D scene representation in computer vision and robotics, enabling accurate inference of geometry, 3D semantics, and dynamics from posed 2D data. Leveraging differentiable rendering, Neural Fields encompass both continuous implicit and explicit neural representations enabling high-fidelity 3D reconstruction, integration of multi-modal sensor data, and generation of novel viewpoints. This survey explores their applications in robotics, emphasizing their potential to enhance perception, planning, and control. Their compactness, memory efficiency, and differentiability, along with seamless integration with foundation and generative models, make them ideal for real-time applications, improving robot adaptability and decision-making. This paper provides a thorough review of Neural Fields in robotics, categorizing applications across various domains and evaluating their strengths and limitations, based on over 200 papers. First, we present four key Neural Fields frameworks: Occupancy Networks, Signed Distance Fields, Neural Radiance Fields, and Gaussian Splatting. Second, we detail Neural Fields' applications in five major robotics domains: pose estimation, manipulation, navigation, physics, and autonomous driving, highlighting key works and discussing takeaways and open challenges. Finally, we outline the current limitations of Neural Fields in robotics and propose promising directions for future research. Project page: https://robonerf.github.io

Foundation models have transformed machine learning for language and vision, but achieving comparable impact in physical simulation remains a challenge. Data heterogeneity and unstable long-term dynamics inhibit learning from sufficiently diverse dynamics, while varying resolutions and dimensionalities challenge efficient training on modern hardware. Through empirical and theoretical analysis, we incorporate new approaches to mitigate these obstacles, including a harmonic-analysis-based stabilization method, load-balanced distributed 2D and 3D training strategies, and compute-adaptive tokenization. Using these tools, we develop Walrus, a transformer-based foundation model developed primarily for fluid-like continuum dynamics. Walrus is pretrained on nineteen diverse scenarios spanning astrophysics, geoscience, rheology, plasma physics, acoustics, and classical fluids. Experiments show that Walrus outperforms prior foundation models on both short and long term prediction horizons on downstream tasks and across the breadth of pretraining data, while ablation studies confirm the value of our contributions to forecast stability, training throughput, and transfer performance over conventional approaches. Code and weights are released for community use.

Neural networks are a powerful class of nonlinear functions that can be trained end-to-end on various applications. While the over-parametrization nature in many neural networks renders the ability to fit complex functions and the strong representation power to handle challenging tasks, it also leads to highly correlated neurons that can hurt the generalization ability and incur unnecessary computation cost. As a result, how to regularize the network to avoid undesired representation redundancy becomes an important issue. To this end, we draw inspiration from a well-known problem in physics -- Thomson problem, where one seeks to find a state that distributes N electrons on a unit sphere as evenly as possible with minimum potential energy. In light of this intuition, we reduce the redundancy regularization problem to generic energy minimization, and propose a minimum hyperspherical energy (MHE) objective as generic regularization for neural networks. We also propose a few novel variants of MHE, and provide some insights from a theoretical point of view. Finally, we apply neural networks with MHE regularization to several challenging tasks. Extensive experiments demonstrate the effectiveness of our intuition, by showing the superior performance with MHE regularization.

Protein-ligand binding affinity prediction is essential for drug discovery and toxicity assessment. While machine learning (ML) promises fast and accurate predictions, its progress is constrained by the availability of reliable data. In contrast, physics-based methods such as absolute binding free energy perturbation (AB-FEP) deliver high accuracy but are computationally prohibitive for high-throughput applications. To bridge this gap, we introduce ToxBench, the first large-scale AB-FEP dataset designed for ML development and focused on a single pharmaceutically critical target, Human Estrogen Receptor Alpha (ERalpha). ToxBench contains 8,770 ERalpha-ligand complex structures with binding free energies computed via AB-FEP with a subset validated against experimental affinities at 1.75 kcal/mol RMSE, along with non-overlapping ligand splits to assess model generalizability. Using ToxBench, we further benchmark state-of-the-art ML methods, and notably, our proposed DualBind model, which employs a dual-loss framework to effectively learn the binding energy function. The benchmark results demonstrate the superior performance of DualBind and the potential of ML to approximate AB-FEP at a fraction of the computational cost.

This review gives an overview of the development of machine learning in geoscience. A thorough analysis of the co-developments of machine learning applications throughout the last 70 years relates the recent enthusiasm for machine learning to developments in geoscience. I explore the shift of kriging towards a mainstream machine learning method and the historic application of neural networks in geoscience, following the general trend of machine learning enthusiasm through the decades. Furthermore, this chapter explores the shift from mathematical fundamentals and knowledge in software development towards skills in model validation, applied statistics, and integrated subject matter expertise. The review is interspersed with code examples to complement the theoretical foundations and illustrate model validation and machine learning explainability for science. The scope of this review includes various shallow machine learning methods, e.g. Decision Trees, Random Forests, Support-Vector Machines, and Gaussian Processes, as well as, deep neural networks, including feed-forward neural networks, convolutional neural networks, recurrent neural networks and generative adversarial networks. Regarding geoscience, the review has a bias towards geophysics but aims to strike a balance with geochemistry, geostatistics, and geology, however excludes remote sensing, as this would exceed the scope. In general, I aim to provide context for the recent enthusiasm surrounding deep learning with respect to research, hardware, and software developments that enable successful application of shallow and deep machine learning in all disciplines of Earth science.

Matbench Discovery simulates the deployment of machine learning (ML) energy models in a high-throughput search for stable inorganic crystals. We address the disconnect between (i) thermodynamic stability and formation energy and (ii) in-domain vs out-of-distribution performance. Alongside this paper, we publish a Python package to aid with future model submissions and a growing online leaderboard with further insights into trade-offs between various performance metrics. To answer the question which ML methodology performs best at materials discovery, our initial release explores a variety of models including random forests, graph neural networks (GNN), one-shot predictors, iterative Bayesian optimizers and universal interatomic potentials (UIP). Ranked best-to-worst by their test set F1 score on thermodynamic stability prediction, we find CHGNet > M3GNet > MACE > ALIGNN > MEGNet > CGCNN > CGCNN+P > Wrenformer > BOWSR > Voronoi tessellation fingerprints with random forest. The top 3 models are UIPs, the winning methodology for ML-guided materials discovery, achieving F1 scores of ~0.6 for crystal stability classification and discovery acceleration factors (DAF) of up to 5x on the first 10k most stable predictions compared to dummy selection from our test set. We also highlight a sharp disconnect between commonly used global regression metrics and more task-relevant classification metrics. Accurate regressors are susceptible to unexpectedly high false-positive rates if those accurate predictions lie close to the decision boundary at 0 eV/atom above the convex hull where most materials are. Our results highlight the need to focus on classification metrics that actually correlate with improved stability hit rate.

Molecular representation is a foundational element in our understanding of the physical world. Its importance ranges from the fundamentals of chemical reactions to the design of new therapies and materials. Previous molecular machine learning models have employed strings, fingerprints, global features, and simple molecular graphs that are inherently information-sparse representations. However, as the complexity of prediction tasks increases, the molecular representation needs to encode higher fidelity information. This work introduces a novel approach to infusing quantum-chemical-rich information into molecular graphs via stereoelectronic effects. We show that the explicit addition of stereoelectronic interactions significantly improves the performance of molecular machine learning models. Furthermore, stereoelectronics-infused representations can be learned and deployed with a tailored double graph neural network workflow, enabling its application to any downstream molecular machine learning task. Finally, we show that the learned representations allow for facile stereoelectronic evaluation of previously intractable systems, such as entire proteins, opening new avenues of molecular design.

Neural field methods have seen great progress in various long-standing tasks in computer vision and computer graphics, including novel view synthesis and geometry reconstruction. As existing neural field methods try to predict some coordinate-based continuous target values, such as RGB for Neural Radiance Field (NeRF), all of these methods are regression models and are optimized by some regression loss. However, are regression models really better than classification models for neural field methods? In this work, we try to visit this very fundamental but overlooked question for neural fields from a machine learning perspective. We successfully propose a novel Neural Field Classifier (NFC) framework which formulates existing neural field methods as classification tasks rather than regression tasks. The proposed NFC can easily transform arbitrary Neural Field Regressor (NFR) into its classification variant via employing a novel Target Encoding module and optimizing a classification loss. By encoding a continuous regression target into a high-dimensional discrete encoding, we naturally formulate a multi-label classification task. Extensive experiments demonstrate the impressive effectiveness of NFC at the nearly free extra computational costs. Moreover, NFC also shows robustness to sparse inputs, corrupted images, and dynamic scenes.

There is great potential to apply machine learning in the area of numerical lattice quantum field theory, but full exploitation of that potential will require new strategies. In this white paper for the Snowmass community planning process, we discuss the unique requirements of machine learning for lattice quantum field theory research and outline what is needed to enable exploration and deployment of this approach in the future.

In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating Lagrangians as complex, rule-based constructs similar to linguistic expressions, we trained a transformer model -- proven to be effective in natural language tasks -- to predict the Lagrangian corresponding to a given list of particles. We report on the transformer's performance in constructing Lagrangians respecting the Standard Model SU(3)times SU(2)times U(1) gauge symmetries. The resulting model is shown to achieve high accuracies (over 90\%) with Lagrangians up to six matter fields, with the capacity to generalize beyond the training distribution, albeit within architectural constraints. We show through an analysis of input embeddings that the model has internalized concepts such as group representations and conjugation operations as it learned to generate Lagrangians. We make the model and training datasets available to the community. An interactive demonstration can be found at: https://huggingface.co/spaces/JoseEliel/generate-lagrangians.

Large language models are emerging as powerful tools for scientific law discovery, a foundational challenge in AI-driven science. However, existing benchmarks for this task suffer from a fundamental methodological trilemma, forcing a trade-off between scientific relevance, scalability, and resistance to memorization. Furthermore, they oversimplify discovery as static function fitting, failing to capture the authentic scientific process of uncovering embedded laws through the interactive exploration of complex model systems. To address these critical gaps, we introduce NewtonBench, a benchmark comprising 324 scientific law discovery tasks across 12 physics domains. Our design mitigates the evaluation trilemma by using metaphysical shifts - systematic alterations of canonical laws - to generate a vast suite of problems that are scalable, scientifically relevant, and memorization-resistant. Moreover, we elevate the evaluation from static function fitting to interactive model discovery, requiring agents to experimentally probe simulated complex systems to uncover hidden principles. Our extensive experiment reveals a clear but fragile capability for discovery in frontier LLMs: this ability degrades precipitously with increasing system complexity and exhibits extreme sensitivity to observational noise. Notably, we uncover a paradoxical effect of tool assistance: providing a code interpreter can hinder more capable models by inducing a premature shift from exploration to exploitation, causing them to satisfice on suboptimal solutions. These results demonstrate that robust, generalizable discovery in complex, interactive environments remains the core challenge. By providing a scalable, robust, and scientifically authentic testbed, NewtonBench offers a crucial tool for measuring true progress and guiding the development of next-generation AI agents capable of genuine scientific discovery.

Molecular docking is critical to structure-based virtual screening, yet the throughput of such workflows is limited by the expensive optimization of scoring functions involved in most docking algorithms. We explore how machine learning can accelerate this process by learning a scoring function with a functional form that allows for more rapid optimization. Specifically, we define the scoring function to be the cross-correlation of multi-channel ligand and protein scalar fields parameterized by equivariant graph neural networks, enabling rapid optimization over rigid-body degrees of freedom with fast Fourier transforms. The runtime of our approach can be amortized at several levels of abstraction, and is particularly favorable for virtual screening settings with a common binding pocket. We benchmark our scoring functions on two simplified docking-related tasks: decoy pose scoring and rigid conformer docking. Our method attains similar but faster performance on crystal structures compared to the widely-used Vina and Gnina scoring functions, and is more robust on computationally predicted structures. Code is available at https://github.com/bjing2016/scalar-fields.

In this paper, we introduce a mesh-free two-level hybrid Tucker tensor format for approximation of multivariate functions, which combines the product Chebyshev interpolation with the ALS-based Tucker decomposition of the tensor of Chebyshev coefficients. It allows to avoid the expenses of the rank-structured approximation of function-related tensors defined on large spacial grids, while benefiting from the Tucker decomposition of the rather small core tensor of Chebyshev coefficients. This leads to nearly optimal Tucker rank parameters which are close to the results for well established Tucker-ALS algorithm applied to the large grid-based tensors. These rank parameters inherited from the Tucker-ALS decomposition of the coefficient tensor can be much less than the polynomial degrees of the initial Chebyshev interpolant via function independent basis set. Furthermore, the tensor product Chebyshev polynomials discretized on a tensor grid leads to a low-rank two-level orthogonal algebraic Tucker tensor that approximates the initial function with controllable accuracy. It is shown that our techniques could be gainfully applied to the long-range part of the electrostatic potential of multi-particle systems approximated in the range-separated tensor format. Error and complexity estimates of the proposed methods are presented. We demonstrate the efficiency of the suggested method numerically on examples of the long-range components of multi-particle interaction potentials generated by 3D Newton kernel for large bio-molecule systems and lattice-type compounds.

We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as quality and quantity of the training dataset, network storage and noise, that is valid in the limit of large network size and structureless datasets: these networks may work in a ultra-storage regime (where they can handle a huge amount of patterns, if compared with shallow neural networks) or in a ultra-detection regime (where they can perform pattern recognition at prohibitive signal-to-noise ratios, if compared with shallow neural networks). Guided by the random theory as a reference framework, we also test numerically learning, storing and retrieval capabilities shown by these networks on structured datasets as MNist and Fashion MNist. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate supervised learning in neural networks, beyond the shallow limit, in general.

Estimating physical properties for visual data is a crucial task in computer vision, graphics, and robotics, underpinning applications such as augmented reality, physical simulation, and robotic grasping. However, this area remains under-explored due to the inherent ambiguities in physical property estimation. To address these challenges, we introduce GaussianProperty, a training-free framework that assigns physical properties of materials to 3D Gaussians. Specifically, we integrate the segmentation capability of SAM with the recognition capability of GPT-4V(ision) to formulate a global-local physical property reasoning module for 2D images. Then we project the physical properties from multi-view 2D images to 3D Gaussians using a voting strategy. We demonstrate that 3D Gaussians with physical property annotations enable applications in physics-based dynamic simulation and robotic grasping. For physics-based dynamic simulation, we leverage the Material Point Method (MPM) for realistic dynamic simulation. For robot grasping, we develop a grasping force prediction strategy that estimates a safe force range required for object grasping based on the estimated physical properties. Extensive experiments on material segmentation, physics-based dynamic simulation, and robotic grasping validate the effectiveness of our proposed method, highlighting its crucial role in understanding physical properties from visual data. Online demo, code, more cases and annotated datasets are available on https://Gaussian-Property.github.io{this https URL}.

In this paper, we explore the application of mean field theory, a technique from statistical physics, to deep metric learning and address the high training complexity commonly associated with conventional metric learning loss functions. By adapting mean field theory for deep metric learning, we develop an approach to design classification-based loss functions from pair-based ones, which can be considered complementary to the proxy-based approach. Applying the mean field theory to two pair-based loss functions, we derive two new loss functions, MeanFieldContrastive and MeanFieldClassWiseMultiSimilarity losses, with reduced training complexity. We extensively evaluate these derived loss functions on three image-retrieval datasets and demonstrate that our loss functions outperform baseline methods in two out of the three datasets.

Coarse-grained (CG) molecular models of proteins can substantially increase the time and length scales accessible to molecular dynamics simulations of proteins, but recovery of accurate all-atom (AA) ensembles from CG simulation trajectories can be essential for exposing molecular mechanisms of folding and docking and for calculation of physical properties requiring atomistic detail. The recently reported deep generative model FlowBack restores AA detail to protein C-alpha traces using a flow-matching architecture and demonstrates state-of-the-art performance in generation of AA structural ensembles. Training, however, is performed exclusively on structural data and the absence of any awareness of interatomic energies or forces within training results in small fractions of incorrect bond lengths, atomic clashes, and otherwise high-energy structures. In this work, we introduce FlowBack-Adjoint as a lightweight enhancement that upgrades the pre-trained FlowBack model through a one-time, physics-aware post-training pass. Auxiliary contributions to the flow introduce physical awareness of bond lengths and Lennard-Jones interactions and gradients of a molecular mechanics force field energy are incorporated via adjoint matching to steer the FlowBack-Adjoint vector field to produce lower-energy configurations. In benchmark tests against FlowBack, FlowBack-Adjoint lowers single-point energies by a median of ~78 kcal/mol.residue, reduces errors in bond lengths by >92%, eliminates >98% of molecular clashes, maintains excellent diversity of the AA configurational ensemble, and produces configurations capable of initializing stable all-atom molecular dynamics simulations without requiring energy relaxation. We propose FlowBack-Adjoint as an accurate and efficient physics-aware deep generative model for AA backmapping from C-alpha traces.

Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.

We present a method for computing free-energy differences using thermodynamic integration with a neural network potential that interpolates between two target Hamiltonians. The interpolation is defined at the sample distribution level, and the neural network potential is optimized to match the corresponding equilibrium potential at every intermediate time-step. Once the interpolating potentials and samples are well-aligned, the free-energy difference can be estimated using (neural) thermodynamic integration. To target molecular systems, we simultaneously couple Lennard-Jones and electrostatic interactions and model the rigid-body rotation of molecules. We report accurate results for several benchmark systems: a Lennard-Jones particle in a Lennard-Jones fluid, as well as the insertion of both water and methane solutes in a water solvent at atomistic resolution using a simple three-body neural-network potential.

Models based on machine learning can enable accurate and fast molecular property predictions, which is of interest in drug discovery and material design. Various supervised machine learning models have demonstrated promising performance, but the vast chemical space and the limited availability of property labels make supervised learning challenging. Recently, unsupervised transformer-based language models pretrained on a large unlabelled corpus have produced state-of-the-art results in many downstream natural language processing tasks. Inspired by this development, we present molecular embeddings obtained by training an efficient transformer encoder model, MoLFormer, which uses rotary positional embeddings. This model employs a linear attention mechanism, coupled with highly distributed training, on SMILES sequences of 1.1 billion unlabelled molecules from the PubChem and ZINC datasets. We show that the learned molecular representation outperforms existing baselines, including supervised and self-supervised graph neural networks and language models, on several downstream tasks from ten benchmark datasets. They perform competitively on two others. Further analyses, specifically through the lens of attention, demonstrate that MoLFormer trained on chemical SMILES indeed learns the spatial relationships between atoms within a molecule. These results provide encouraging evidence that large-scale molecular language models can capture sufficient chemical and structural information to predict various distinct molecular properties, including quantum-chemical properties.

Evaluating the scientific discovery capabilities of large language model based agents, particularly how they cope with varying environmental complexity and utilize prior knowledge, requires specialized benchmarks currently lacking in the landscape. To address this gap, we introduce PhysGym, a novel benchmark suite and simulation platform for rigorously assessing LLM-based scientific reasoning in interactive physics environments. PhysGym's primary contribution lies in its sophisticated control over the level of prior knowledge provided to the agent. This allows researchers to dissect agent performance along axes including the complexity of the problem and the prior knowledge levels. The benchmark comprises a suite of interactive simulations, where agents must actively probe environments, gather data sequentially under constraints and formulate hypotheses about underlying physical laws. PhysGym provides standardized evaluation protocols and metrics for assessing hypothesis accuracy and model fidelity. We demonstrate the benchmark's utility by presenting results from baseline LLMs, showcasing its ability to differentiate capabilities based on varying priors and task complexity.

In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function (RBF) layers combined with an attention mechanism designed to effectively capture nonlinear inter-dependencies inherent in the attractor's temporal evolution. Our results demonstrate successful prediction of the attractor's trajectory across 100 predictions made using a real-world dataset of 36,700 time-series observations encompassing approximately 28 minutes of activity. To further illustrate the performance of our proposed technique, we provide comprehensive visualizations depicting the attractor's original and predicted behaviors alongside quantitative measures comparing observed versus estimated outcomes. Overall, this work showcases the potential of advanced machine learning algorithms in elucidating hidden structures in complex physical systems while offering practical applications in various domains requiring accurate short-term forecasting capabilities.

Meta-learning enables algorithms to quickly learn a newly encountered task with just a few labeled examples by transferring previously learned knowledge. However, the bottleneck of current meta-learning algorithms is the requirement of a large number of meta-training tasks, which may not be accessible in real-world scenarios. To address the challenge that available tasks may not densely sample the space of tasks, we propose to augment the task set through interpolation. By meta-learning with task interpolation (MLTI), our approach effectively generates additional tasks by randomly sampling a pair of tasks and interpolating the corresponding features and labels. Under both gradient-based and metric-based meta-learning settings, our theoretical analysis shows MLTI corresponds to a data-adaptive meta-regularization and further improves the generalization. Empirically, in our experiments on eight datasets from diverse domains including image recognition, pose prediction, molecule property prediction, and medical image classification, we find that the proposed general MLTI framework is compatible with representative meta-learning algorithms and consistently outperforms other state-of-the-art strategies.

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Machine learning (ML) is increasingly used in structural engineering and design, yet its broader adoption is hampered by the lack of openly accessible datasets of structural systems. We introduce BridgeNet, a publicly available graph-based dataset of 20,000 form-found bridge structures aimed at enabling Graph ML and multi-modal learning in the context of conceptual structural design. Each datapoint consists of (i) a pin-jointed equilibrium wireframe model generated with the Combinatorial Equilibrium Modeling (CEM) form-finding method, (ii) a volumetric 3D mesh obtained through force-informed materialization, and (iii) rendered images from two canonical camera angles. The resulting dataset is modality-rich and application-agnostic, supporting tasks such as CEM-specific edge classification and parameter inference, surrogate modeling of form-finding, cross-modal reconstruction between graphs, meshes and images, and generative structural design. BridgeNet addresses a key bottleneck in data-driven applications for structural engineering and design by providing a dataset that facilitates the development of new ML-based approaches for equilibrium bridge structures.

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in graphs such as large conjugated molecules, and social networks due to oversmoothing and oversquashing. Although Spectral GNNs and traditional neural networks such as recurrent neural networks and transformers mitigate these challenges, they often lack generalizability, or fail to capture detailed structural relationships or symmetries in the data. To address these concerns, we introduce Matrix Function Neural Networks (MFNs), a novel architecture that parameterizes non-local interactions through analytic matrix equivariant functions. Employing resolvent expansions offers a straightforward implementation and the potential for linear scaling with system size. The MFN architecture achieves stateof-the-art performance in standard graph benchmarks, such as the ZINC and TU datasets, and is able to capture intricate non-local interactions in quantum systems, paving the way to new state-of-the-art force fields.