Machine Learning Interatomic Potentials

Also known as MLIP

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5 papers in the last four weeks, up 67% on the four weeks before. 0.0% of all new papers.

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Latest papers 55

Oct 7, 2026cond-mat.mtrl-sci

Origins of Universal Machine Learning Force-Field Errors in Multicomponent Materials

Universal machine learning force-field generalization to multicomponent environments generated by compositional design remains insufficiently assessed. We construct a benchmark of 7,599 multicomponent configurations inspired by high-entropy design, elemental substitution and anion mixing. Eleven pretrained models are evaluated against density functional theory for energies, forces and stresses, with assessment extended to elastic, vibrational and adsorption-related properties. Force errors are analysed through training-reference coverage, local geometric heterogeneity, distance directionality and elemental response. Distances to training-reference environments reveal a qualitative association between coverage differences and increasing errors, while substantial variation remains at similar distances. Higher-error groups show greater local geometric heterogeneity, although OMat24 provides broad coverage of these environments. Relative to training-reference pair medians, errors remain low near the median, rise steeply on the compression side and increase more weakly on the extension side. After matching element pairs and absolute distance deviations, compression-side force errors are 1.81-1.95 times extension-side errors. Model-predicted pairwise interaction curves show greater curvature under compression. Fitting difficulty in independent elemental systems correlates with electronic band-energy responses to atomic displacements and Fermi-level shifts, and a similar pattern is observed in multicomponent systems. In parameter-matched comparisons, spherical-harmonic representations with maximum degrees of 2 and 4 lower test force errors for 38 and 40 of 43 elements, respectively, while differences in elemental difficulty remain. These findings inform force-field selection for experimental compositional design and identify targets for training-data sampling and model representations.

Hongwei Du, Dingyang Lv, Baole Wei +11

Zhongguancun Academy, Beijing 100094, China. · Zhongguancun Institute of Artificial Intelligence, Beijing 100094, China. · Kairos Materials, Beijing, 100094, China. +4

Machine Learning Interatomic Potentials Materials Science

Oct 5, 2026cs.LG

FlashCart: Fast Cartesian Tensor Products for Equivariant Interatomic Potentials

Machine-learned interatomic potentials extend atomistic simulations beyond the length- and timescales accessible to electronic-structure methods. However, the computational cost of equivariant architectures limits the local correlations they can represent in practice and therefore their achievable accuracy. Here we introduce FlashCart, which makes higher-order correlations affordable by combining generated GPU kernels with an architecture that recursively builds equivariant features and compresses them to a fixed width at each step. We express tensor products in independent Cartesian components and symbolically simplify them and their derivatives, producing fused kernels that often outperform optimized spherical counterparts. We then show that increasing correlation order improves accuracy more efficiently than increasing width, depth, or tensor rank. On SPICE-MACE-OFF, FlashCart models advance the measured accuracy-efficiency frontier: a model with

5.6

million parameters achieves lower energy and force errors and

10\times

faster inference than a transformer with

189

million parameters.

Viktor Zaverkin, Payman Goodarzi, Sergey V. Sukhomlinov +4

INM – Leibniz Institute for New Materials · Saarland University · German Research Center for Artificial Intelligence (DFKI) +2

Machine Learning Interatomic Potentials GPU Kernel Optimization Equivariant GNNs

Oct 5, 2026cs.LG

Langevin Flow Maps: Efficient Molecular Dynamics and Transition Path Sampling

Molecular dynamics simulations proceed by integrating the Langevin equations over many small femtosecond timesteps. This poses a challenge for estimating ensemble properties and transition dynamics that occur on much longer timescales. We introduce Langevin Flow Maps, which extend machine-learned force-fields to additionally learn the stochastic Langevin integrator. We show that Langevin Flow Maps enable large-timestep molecular dynamics and recover accurate dynamical properties of the system, while running an order of magnitude faster than current machine-learned force fields. Further, by training on a diverse molecular dataset, we demonstrate a path towards transferable Langevin Flow Maps.

Sam McCallum, Niklas Rindtorff, Alexander Tong +1

University of Bath · AITHYRA

Stochastic Differential Equations Machine Learning Interatomic Potentials Langevin Dynamics Flow Map Learning Molecular Dynamics Simulation

Oct 1, 2026cs.LG

BranchIP: Learning Adaptive Equivariant Computation for Interatomic Potentials

Equivariant machine learning interatomic potentials (MLIPs) have revolutionized atomistic modeling, but accurate treatment of complex materials and molecular systems demands expensive models. This limits simulation length- and time-scales, with tensor products a key computational bottleneck. The recent emergence of foundation-scale MLIPs further exacerbates this challenge. We present Branch Interatomic Potential (BranchIP), a single-model framework for learned adaptive tensor product computation, trained with a novel distillation loss. In our experiments on two systems of physical interest, a heterogeneous catalysis system and a proton-conducting solid acid electrolyte, BranchIP accelerates MLIPs across model sizes by up to

2.4\times

while reducing memory usage by up to

2.6\times

. This is achieved while maintaining physical fidelity. Furthermore, the learned adaptive computation provides model interpretability by revealing which interactions demand deeper computation and showing how computational depth relates to chemical complexity and dynamics.

Laura Zichi, Gil Harari, Chuin Wei Tan +6

Harvard University · Robert Bosch LLC Research and Technology Center

Machine Learning Interatomic Potentials Equivariant Neural Networks Adaptive Computation Computational Materials Science

Sep 30, 2026physics.chem-ph

A strategic roadmap for an atomistic machine-learning ecosystem

Data-driven machine learning (ML) techniques have become an essential tool in many domains of science. Their application to atomistic simulations of matter is particularly widespread and impactful. This success is due largely to the existence of a well-developed and established physics-based modeling framework, ranging from first-principles electronic-structure calculations to molecular dynamics and statistical sampling, into which ML was integrated naturally to reshape long-standing trade-offs between accuracy, efficiency, and scale. Nevertheless, this integration raises both conceptual and practical challenges, from choosing between data-centric and physics-based modeling approaches to adapting established software stacks to modern hardware accelerators and ML libraries. As the field evolves rapidly, fueled in part by widespread enthusiasm but also by tangible impact, it seems appropriate to take a moment to consider the current state of the art and open challenges, and reflect on what can be done to better coordinate efforts across the community. With this goal in mind, several members of this community met in Lausanne in January 2026 at CECAM to discuss algorithms, models, software and hardware infrastructure, and the most promising scientific applications that have become possible thanks to the use of artificial intelligence in atomic-scale simulations. This strategic roadmap paper summarizes the outcomes of these discussions, suggesting some long-term goals, and some concrete actions, to establish a healthy, sustainable and impactful atomistic ML ecosystem.

Jörg Behler, Michele Ceriotti, Cecilia Clementi +46

Machine Learning Interatomic Potentials Scientific ML Computational Materials Science

Sep 23, 2026cond-mat.mtrl-sci

SoLiD26: A First Principles Solid-Liquid Interface Dataset for Machine-learned Interatomic Potentials

Machine-learned interatomic potentials (MLIPs) for solid-liquid interfaces in advanced materials applications, e.g., electrochemistry, catalysis and corrosion, require training data that samples both liquid environments, the solid and the interface itself. We present SoLiD26, a curated solid-liquid interface dataset, containing 15.4 million first-principles atomic structures with up to 576 atoms and 15 chemical elements for training and evaluating MLIPs. The structures were compiled from density functional theory (DFT) calculations performed in studies of solid-liquid interfaces, with most configurations originating from ab initio molecular dynamics (AIMD) simulations. Each record contains atomic species, positions, simulation cell, periodic boundary conditions, potential energy and atomic forces. SoLiD26 includes aqueous coinage metal interfaces, electrode-electrolyte systems, and selected bulk reference structures, calculated with VASP using the PBE functional and D3 dispersion corrections. We describe the data ingestion and preparation pipeline used to construct the dataset. The application of SoLiD26 for training and evaluating MLIPs is demonstrated with a suite of MACE models on a simple training, validation and test split. The dataset enables development and benchmarking of MLIPs for structurally and chemically heterogeneous solid-liquid interfaces.

Jonas Busk, Emil J. P. Frost, Yogeshwaran Krishnan +7

Department of Energy Conversion and Storage, Technical University of Denmark, Kongens Lyngby, Denmark. · Pioneer Center for Accelerating P2X Materials Discovery (CAPeX), Technical University of Denmark, Kongens Lyngby, Denmark.

Machine Learning Interatomic Potentials Materials Science Computational Materials Science

Sep 17, 2026physics.chem-ph

Truncated automatic sparse differentiation for machine learning interatomic potentials

Machine learning interatomic potentials (MLIPs) learn the mapping from atomic positions to potential energy. The forces, the negative gradient of this energy, drive molecular dynamics and are readily obtained using automatic differentiation. Higher-order derivatives, most notably the Hessian, describe collective motion and allow the direct prediction of experimental observables, but are considered computationally inaccessible for large systems. We suggest a solution: in physical systems, interactions decay with distance, and most MLIPs build on this locality through message passing up to a finite receptive field. This implies both sparsity of higher-order derivatives and their decay with distance. This structure can be exploited using automatic sparse differentiation (ASD). We explain how to compute the sparsity pattern for MLIP derivatives and demonstrate that, for multiple foundation MLIPs, ASD computes full Hessians of large porous materials exactly, but with modest speedups at best. The larger gains come from truncated ASD: discarding small, but nonzero, Hessian entries between distant atoms yields order-of-magnitude speedups with negligible impact on predicted observables.

Marcel F. Langer, Adrian Hill, Michele Ceriotti

Laboratory of Computational Science and Modeling (COSMO), EPFL, Lausanne, Switzerland · Machine Learning Group, Technical University of Berlin, Berlin, Germany · BIFOLD – Berlin Institute for the Foundations of Learning and Data, Berlin, Germany

Automatic Differentiation Machine Learning Interatomic Potentials Computational Materials Science

Sep 8, 2026cs.LG

MLIP Detective: Active Failure Mode Discovery Beyond Benchmark Scores for Machine-Learning Interatomic Potentials

Universal machine-learning interatomic potentials (u-MLIPs) aim to generalize across diverse configurations. Benchmarks enable reproducible evaluation but may not expose failures outside their predefined scope. Here, we show that physics-informed search can complement benchmark-based evaluation by uncovering hidden failure modes. We introduce MLIP Detective, an agentic framework for active failure mode discovery. Starting from benchmark evidence, MLIP Detective generates falsifiable, physics-informed failure hypotheses, screens them with inexpensive simulations, and escalates only the most suspicious cases to human experts together with proposed verification protocols. Without issue-specific prompting, MLIP Detective identified and characterized a systematic anomaly in MACE-MPA-0: the model predicted some relaxed adsorbate-surface systems involving O- or F-containing adsorbates to be higher in energy than their corresponding separated fragments. Using cross-model comparisons, MLIP Detective further inferred a likely training-data origin for the anomaly, consistent with recent reports.

Ryuhei Okuno, Nontawat Charoenphakdee, Kaoru Hisama +1

Preferred Networks

AI Agents for Scientific Discovery Machine Learning Interatomic Potentials

Sep 4, 2026cs.LG

Hessian-based molecular conformation augmentation for a scalable and efficient strategy of machine learning interatomic potentials

While machine-learning interatomic potentials (MLIPs) have successfully learned potential energy surfaces (PES) and atomic forces, many practical applications, such as vibrational analysis and transition state search, rely heavily on the PES Hessian. Yet standard MLIPs are trained on energy and forces alone, and existing methods that incorporate the Hessian into training objectives require architectural modifications and incur significant computational and memory overheads from higher-order backpropagation. To address these limitations, we propose two Hessian-derived data augmentation schemes: isotropic Gaussian displacement (\textbf{UniAug}) and normal mode-weighted displacement (\textbf{ModeAug}). Both methods utilize simple Taylor expansions, achieving effective augmentation without altering training objectives or extending the autograd graph. This allows seamless, plug-and-play integration with existing architectures and training pipelines. Comprehensive evaluations across non-equilibrium and equilibrium datasets demonstrate that our approach enhances model accuracy where reference forces are large while providing practical, task-specific guidelines.

Bumju Kwak, Jeonghee Jo

Independent researcher, Seoul, Republic of Korea

Data Augmentation Machine Learning Interatomic Potentials

Sep 1, 2026cs.LG

Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials

We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that

L

layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full

L

-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.

Pingbing Ming, Han Wang

SKLMS, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, No. 55, East Road Zhong-Guan-Cun, Beijing 100190, China · National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Beijing 100094, P.R. China, and HEDPS, CAPT, College of Engineering, Peking University, Beijing 100871, P.R. China

Machine Learning Interatomic Potentials GNN Expressivity Message Passing Neural Networks Hypergraph Neural Networks Neural Network Approximation Theory

Aug 31, 2026cs.LG

AdaptNTK: Adaptive Uncertainty Quantification and Active Learning for Neural Network Potentials

Machine learning interatomic potentials bridge the gap between quantum chemical precision and classical computational speed, enabling molecular dynamics simulations with first-principles accuracy. Their reliability is often improved through active learning, which iteratively expands the training set by identifying uncertain, out-of-distribution configurations. Existing uncertainty-quantification methods often involve a trade-off between computational cost and reliability, and generally cannot account for redundancy as an acquisition batch is assembled. Here, we introduce AdaptNTK, a single-model framework that measures uncertainty as a regularized Mahalanobis distance in empirical neural tangent kernel (NTK) feature space. With the NTK features fixed during acquisition, the uncertainty depends on the acquired configurations but not their reference labels. This allows the uncertainty to be updated recursively after each selection without retraining, reducing redundancy within an acquisition batch. On held-out rMD17 data, AdaptNTK achieves the highest mean correlations with force errors (Spearman 0.68, Pearson 0.71) and matches a three-member ensemble in error retention. In active learning experiments, AdaptNTK achieves the lowest force errors across rMD17 and Transition-1X, with particularly strong performance on transition-state configurations in Transition-1X. AdaptNTK provides a 2.6-fold speedup per Transition-1X cycle relative to the ensemble, providing efficient single-model uncertainty estimation with sequential updates for data-efficient active learning.

Prajwal Ananth, Shuwen Yue

Center for Applied Mathematics, Cornell University, Ithaca, NY, USA · R. F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY, USA

Uncertainty Quantification Machine Learning Interatomic Potentials Active Learning Neural Tangent Kernel

Jul 31, 2026cs.LG

Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations

We introduce implicit machine learning force fields (I-MLFFs), which replace explicit stacks of neural network layers with self-consistent fixed-point equations. In molecular simulations, this formulation enables intermediate representations to be reused across successive timesteps, thereby warm-starting force evaluation. The resulting models effectively combine the computational footprint of a shallow, single-layer MLFF with the representational capacity and accuracy of a deep neural network. Our approach unlocks architecture-agnostic efficiency gains that are inaccessible when force prediction and trajectory integration are considered separately. We demonstrate this across three major classes of graph neural networks: invariant, equivariant Cartesian tensor, and SO(3)-equivariant spherical-tensor architectures. Each yields a two- to five-fold reduction in compute and memory footprint. Crucially, these gains are achieved while retaining full atomistic resolution and the original integration timestep, avoiding spatial or temporal coarse graining. Our contribution therefore advances the scaling frontier of quantum-mechanically faithful molecular simulation, enabling longer trajectories and larger atomistic systems within fixed GPU memory and compute budgets, and thereby opening access to new insights across biomolecular and material systems.

Johannes Maeß, Leon Werner, J. Thorben Frank +5

BIFOLD, Berlin, Germany. · Machine Learning Group, TU Berlin, Berlin, Germany. · Department of Artificial Intelligence, Korea University, Seoul, South Korea. +1

Implicit Neural Representations Machine Learning Interatomic Potentials Molecular Dynamics Simulation

Jul 25, 2026cs.AI

An Ontology for Machine Learning Interatomic Potentials

Machine learning interatomic potentials (MLIPs) approximate quantum-mechanical energies and forces---conventionally computed by density functional theory (DFT) or wave-function methods---at a fraction of the cost. The field encompasses a growing ecosystem of algorithms, training datasets, hyperparameters, and target materials, yet the metadata needed to systematically compare, reproduce, and build upon MLIP studies remains scattered across papers, scripts, and ad-hoc file formats. We present the MLIPs ontology, an OWL 2 DL ontology that captures the concepts needed to describe MLIP methods, their hyperparameters, training datasets with DFT provenance, and published benchmarks. The ontology is organized into three modules---Method, Training Data, and Benchmark---and connects existing ontologies in materials science (MDO, CMSO/ASMO) and machine learning (ML-Schema), complementing dataset-side schemas such as Croissant. It declares 27 formal axioms enforcing data completeness and consistency, including property chains that link trained models to their methods and training data. We demonstrate the ontology through a running example based on Moment Tensor Potentials and evaluate it through competency-question execution on a 20-paper seeded knowledge graph, OWL reasoning, and comparison with existing ontologies.

Daniel Hernández, Jong Hyun Jung, Yuji Ikeda +11

Institute for Artificial Intelligence, University of Stuttgart, Germany · Institute for Materials Science, University of Stuttgart, Germany · Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Germany and Department for Computational Materials Design, Max-Planck-Institut for Sustainable Materials, Germany

Machine Learning Interatomic Potentials

Jul 23, 2026physics.chem-ph

Graph-Theoretic Neural Network Fragmentation with Covariant Direct Molecular Force Learning: Enabling Coupled-Cluster Accuracy AIMD for Fluxional Systems

Accurate ab initio molecular dynamics (AIMD) simulations of complex, fluxional chemical systems are severely limited by the high computational scaling of correlated electronic structure methods. To overcome this bottleneck, we present a robust, graph-theoretic molecular fragmentation framework integrated with machine learning to directly model post-Hartree-Fock nuclear forces at coupled cluster accuracy. Bypassing the limitations of automatic differentiation on learned energy surfaces that may struggle with link-atom Jacobians, our approach directly predicts nuclear force vectors. By projecting these vectors onto fragment-fixed principal axes of inertia, we establish co-variant descriptors that naturally preserve rotational, translational, and permutational invariance. The methodology achieves exceptional high parameter efficiency through a vector-valued training protocol that reduces trainable parameters by over an order of magnitude, while an unsupervised mini-batch k-means space tessellation algorithm constructs highly representative training databases using only 10% to 20% of reference configurations. We rigorously validated this framework on the highly fluxional solvated Zundel cation H_{13}O_6^+ ). Our fully machine-learning-predicted AIMD trajectories successfully reproduced complex dynamical signatures and key structural characteristics, including radial distribution functions and the velocity autocorrelation power spectrum. Ultimately, this scalable, systematically improvable framework bridges the gap between high-level correlated wavefunction theories and long-timescale reactive sampling, laying the foundation for advanced, LLM-inspired transfer learning in modern chemical dynamics simulations.

Xiao Zhu, Srinivasan S. Iyengar

Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Ave, Bloomington, IN-47405

Machine Learning Interatomic Potentials Equivariant Neural Networks Molecular Dynamics Simulation

Jul 16, 2026physics.chem-ph

Full-data accuracy with fewer labels for training and fine-tuning machine-learning force fields

Machine-learning force fields (MLFFs) are reliable only near their training distribution, making efficient construction of diverse training sets a major bottleneck for both train-from-scratch and foundation fine-tuning workflows. Active learning can reduce this cost, but standard model-committee uncertainty is impractical for foundation MLFFs because each committee member requires a separate fine-tuning run. We present an active-learning workflow based on last-layer-projection regression (LLPR), a forward-pass-cheap per-configuration uncertainty estimator. Across molecular, condensed-phase, and electrolyte systems, LLPR identifies compact, high-value training sets that recover full-data accuracy using only a small fraction of electronic-structure labels. In foundation-model fine-tuning, LLPR-selected configurations reach the full-pool fine-tuning ceiling with substantially fewer labels than random selection. In iterative electrolyte fine-tuning, LLPR detects unphysical local coordination before DFT labelling, provides an absolute force-error threshold, and enables automatic termination of the learning loop. The resulting models reproduce reference density and ion-coordination structure, providing a scalable uncertainty-quantification strategy across MLFF training regimes.

Sheng Bi, Yi-Ze Wang, Jun Cheng

College of Materials, Xiamen University, Xiamen, China. · Laboratory of AI for Electrochemistry (AI4EC), IKKEM, Xiamen, China. · State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China.

Uncertainty Quantification Machine Learning Interatomic Potentials Active Learning Data-Efficient Learning

Jul 12, 2026physics.chem-ph

Transferable Implicit Solvent Machine Learning Potential for Drugs and Proteins Approaching Ab Initio Accuracy

Machine learning interatomic potentials (MLPs) have revolutionized atomistic modeling, offering the potential to replace traditional methods like Density Functional Theory (DFT). However, inference time of MLPs is orders of magnitude slower than that of classical force fields, hindering real-world applications for biomolecular systems that require timescales of microseconds and beyond. Implicit solvent MLPs can address this issue, but are faced with data challenges associated with coarse-grained modeling. Consequently, previous approaches relied on empirical force field data, thereby inherently limiting the MLP's accuracy. Here, we introduce the Transferable Water Implicit Network (TWIN), an implicit water MLP parametrized entirely by an Equivariant Graph Neural Network and trained solely on ab initio and experimental labels. We demonstrate TWIN's transferability across drug-like molecules, peptides, and proteins, achieving excellent results on ab initio and experimental crystallographic and NMR benchmarks, consistently outperforming previous machine-learning-based implicit solvent or coarse-grained models. Furthermore, TWIN closely matches DFT-based explicit solvent MLPs while providing a two-order-of-magnitude faster timestep evaluation, paving the way for efficient ab initio-level modeling of biomolecular systems in aqueous environments.

Jan Eckwert, Julija Zavadlav

1Multiscale Modeling of Fluid Materials, Department of Engineering Physics and Computation, TUM School of Engineering and Design and Department of Physics, TUM School of Natural Sciences, Technical University of Munich, Munich, 80333, Germany. · 2Atomistic Modeling Center, Munich Data Science Institute, Technical University of Munich, Garching, 85748, Germany.

Machine Learning Interatomic Potentials Molecular Dynamics Simulation

Jul 12, 2026stat.ML

Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials

In this paper, we provide a systematic investigation of SO(2) theory to machine learning interatomic potentials (MLIPs) and identify the limitations of conventional SO(2) Linear architectures relative to SO(3) Clebsch-Gordan Tensor Products (CGTP). Building on these insights, we propose direct Cartesian construction and recursive Clebsch-Gordan construction of Wigner D-matrices and introduce two novel interaction building blocks. First, we propose the Edge Complex Product Basis based on Generalized Asymmetric Contraction, a new formulation for many-body expansion that directly constructs higher-order interactions on edges through complex-valued equivariant multiplications. Second, we introduce Radial Rotary Complex Attention(RRA), which enhances extrapolation performance and surpasses existing attention vector formulations. We also introduce several improvements to the Atomic Cluster Expansion module. Building on these advances, we train our models on OMat24, sAlex, and MPTrj, and introduce TECE-OAM-RRA-1.0, which achieve state-of-the-art (SOTA) performance on the Matbench Discovery.

Zemin Xu, Wenbo Xie, P. Hu

School of Physical Science and Technology, ShanghaiTech University, Shanghai, China · School of Chemistry, Nanjing University, Nanjing, China

Machine Learning Interatomic Potentials Equivariant Neural Networks

Jul 10, 2026cs.LG

Active rejection enables reliable generalization of universal machine-learning interatomic potentials

Universal machine learning interatomic potentials (uMLIPs) bridge quantum-mechanical accuracy and large-scale molecular dynamics, but the cost of high-accuracy calculations such as r

^2

SCAN limits training to datasets that remain small relative to the open materials space. Strong average benchmark performance also does not guarantee reliable energy--force predictions for every structure. We propose Adaptive Multi-Teacher Routing (ATR), which reformulates high-fidelity data construction as a structure-wise decision problem under uncertainty. Using a small set of real r

^2

SCAN labels, ATR calibrates multiple pretrained uMLIP teachers and combines structural descriptors, teacher identity, and inter-teacher disagreement to estimate the reliability of each structure--teacher pair. It selects high-confidence predictions for pseudo-label generation and rejects structures for which no teacher is sufficiently reliable. With real r

^2

SCAN labels for only 0.2% of candidate structures, ATR distils 2.89 million traceable r

^2

SCAN-level pseudo-labels for pretraining. On held-out r

^2

SCAN structures and the MP-r

^2

SCAN benchmark, a lightweight CHGNet trained on the ATR-generated dataset consistently outperforms the baseline and non-routed controls. Finite-temperature molecular dynamics further shows that ATR improves dynamical robustness across multiple material systems, maintaining stable trajectories where baseline simulations undergo catastrophic structural collapse. These results establish active rejection as an effective mechanism for converting multiple pretrained uMLIPs into a scalable and reliable data-construction system for high-fidelity uMLIPs.

Mingxiang Luo, Xinnan Mao, Lu Wang +3

School of Future Information Innovation, Fudan University, Shanghai, China · Shanghai Innovation Institute, Shanghai, China · Suzhou Laboratory, Suzhou, China +1

Machine Learning Interatomic Potentials Selective Prediction Pseudo-Labeling Knowledge Distillation

Jul 6, 2026cs.LG

EquiFiLM: Charge-Conditioned Equivariant Force Fields via Feature-wise Linear Modulation

Foundation machine learning force fields (MLFFs) such as MACE-MP-0 and UMA cover broad chemical space at near density functional theory (DFT) accuracy. However, they assume equilibrium ground-state physics and do not natively handle externally induced changes to the electronic state, such as charging, applied fields, or electronic excitation, which limits their use for driven processes such as photoexcitation and charge injection. We propose EquiFiLM, a lightweight extension that adds continuous external conditioning to any equivariant foundation MLFF via a per-layer Feature-wise Linear Modulation (FiLM) block, learning externally driven changes to the potential energy surface from minimal training data. The block modulates only scalar channels and preserves E(3)-equivariance exactly. We demonstrate the recipe on charged liquid water with the foundation model MACE-MatPES as the backbone, yielding E-MACE. On the four training charges, E-MACE delivers a

3.1\times

reduction in force RMSE (

21.3

to

6.96

meV/

\mathring{A}

) and a

61\times

reduction in per-atom energy RMSE (

6.1

to

0.1

meV/atom) over a baseline without EquiFiLM trained on the same data, at indistinguishable inference cost. Across seven held-out interpolation and extrapolation charges, force RMSE stays within

18-61

meV/

\mathring{A}

and energy RMSE within

0.7-5.4

meV/atom. The model runs stable molecular dynamics across the full range tested and predicts the charge-dependent first-shell response of the reduced pair distribution function probed by ultrafast electron diffraction. Adding this conditioning axis to the foundation requires only a few thousand DFT-labeled frames, against the

\approx 10^8

structures of a charge-aware foundation trained from scratch. The recipe is backbone- and conditioning-agnostic: it applies without architectural change to any equivariant MLFF with scalar interaction-layer channels.

Samuel Sahel-Schackis, Ken-ichi Nomura, Aiichiro Nakano +2

Department of Physics, Stanford University · Collaboratory for Advanced Computing and Simulation, University of Southern California · Linac Coherent Light Source, SLAC National Accelerator Laboratory +1

Machine Learning Interatomic Potentials Equivariant Neural Networks

Jul 2, 2026cs.LG

Beyond Adam: SOAP and Muon for Faster, Label-Efficient Training of Machine Learning Interatomic Potentials

Machine learning interatomic potentials (MLIPs) have become a hallmark of AI for scientific simulation. While efforts on new architectures and datasets have led to increasingly accurate and general models, the choice of optimizer for training has largely remained unexplored, defaulting to Adam and its variants in the community. Here, we implement and systematically compare a class of recently proposed matrix-structured optimizers, including Muon, SOAP, and the hybrid SOAP-Muon, for training NequIP and Allegro MLIP models. We find that these optimizers can substantially outperform Adam in both convergence speed and final accuracy. SOAP and SOAP-Muon emerge as robust and consistently strong methods, while Muon only provides partial gains relative to Adam. The improvements are particularly pronounced under partial force supervision. Our results indicate that optimizer choice is an overlooked yet impactful design axis for MLIPs.

Gil Harari, Yoel Zimmermann, Ola Tangen Kulseng +4

John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA · Robert Bosch LLC Research and Technology Center, Watertown, MA, USA

Machine Learning Interatomic Potentials Neural Network Optimization Muon Optimizer Matrix Optimization

Jul 1, 2026cs.LG

Spin-Weighted Spherical Harmonics Enable Complete and Scalable $\mathrm{E}(3)$ -Equivariant Networks

\mathrm{E}(3)

-equivariant networks are promising for 3D atomistic system modeling, yet their scalability is limited by the

O(L^6)

complexity of the Clebsch-Gordan Tensor Product (CGTP). The recently proposed Gaunt Tensor Product (GTP) reduces the complexity but is unable to capture the antisymmetric paths, resulting in incomplete expressivity. In this work, we present SpinGTP, an approach to overcome the GTP incompleteness by generalizing from scalar functions to Spin-Weighted Spherical Harmonics (SWSH). By relying on the algebraic properties of SWSH, SpinGTP recovers the missing antisymmetric interactions while maintaining the asymptotic efficiency of GTP. It also allows for a more expressive equivariant basis that naturally accounts for the parity-odd components of tensor products. We evaluate SpinGTP across diverse benchmarks, including Tetris, 3BPA, SPICE-MACE-OFF, and OC20. Our results show that SpinGTP achieves accuracies comparable to full CGTP. Notably, by explicitly capturing antisymmetric paths, SpinGTP exhibits superior performance in tasks involving chiral materials and non-centrosymmetric geometries. This work provides a complete, scalable, and mathematically rigorous path toward high-order equivariance in large-scale 3D atomistic system simulations.

Chenxing Liang, Yuchao Lin, Andrii Kryvenko +5

Department of Computer Science and Engineering, Texas A&M University · Lambda, Inc. · Department of Materials Science and Engineering, Texas A&M University +3

Machine Learning Interatomic Potentials Equivariant Neural Networks Equivariant GNNs Spherical Harmonics

Jul 1, 2026physics.chem-ph

Enerzyme: A Framework for Efficient Training of Reactive Neural Network Potentials for Enzyme Catalysis with Application to Methyltransferases

Quantum mechanical (QM) cluster models provide an effective framework for mechanistic studies of enzymatic reactions but remain computationally demanding. Neural network potentials (NNPs) offer a promising route to reduce this cost, but enzymes present challenges beyond small molecules, including large system sizes, implicit-solvent environments, substantial polarization, and charge transfer. Here, we present an integrated software framework for efficient NNP training for mechanistic studies of enzymes, demonstrated on QM cluster models of S-adenosyl-L-methionine-dependent methyltransferases (MTases). Our Enerzyme code introduces modular electrostatics-aware NNP architectures and combines automated QM-cluster construction with reactive dataset generation. The Enerzymette subpackage automates reaction pathway exploration at both NNP and DFT levels. We show that iterative flexible scans and nudged elastic band calculations impose stricter requirements on NNPs than conventional dataset metrics. Nevertheless, NNPs trained on fewer than 1,000 system-specific datapoints reproduce reaction energetics and transition-state structures for MTase clusters containing up to 545 atoms with near-chemical accuracy. Direct supervision of atomic charges and consistent dielectric screening substantially improve simulation stability and accuracy, while multitask-learned atomic charges capture charge transfer and polarization trends and provide chemically meaningful descriptors of reactivity. Finally, transferability across chemically diverse catechol O-methyltransferase substrates indicates that NNPs learn generalizable reactivity patterns as training data expand across multiple enzymes. Together, these results establish a foundation for accelerating enzyme mechanistic studies and guide future NNP development for biomolecular reactivity.

Weiliang Luo, Heather J. Kulik

Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Machine Learning Interatomic Potentials Quantum Chemistry

Jun 28, 2026physics.chem-ph

Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentials

\mathrm{Cl}(3,0)

interatomic potentials, despite their algebraic elegance, predict force magnitudes accurately but force directions poorly. Across ten rMD17 molecules, every

L \leq 1

baseline in our twelve-model study attains aggregate force-cosine similarity below

0.25

. The cause is structural. The geometric product of two vectors in

\mathbb{R}^3

realises only the

L=0

and

L=1

components of its irreducible representation content, leaving the symmetric-traceless rank-2 component absent from the per-edge bilinear that drives each message-passing layer. We address this with CliffordSTF, which couples the Clifford multivector to closed-form symmetric-traceless tensor tracks at ranks two and three through bilinear cross-track contractions, using a single learned bilinear and no Clebsch--Gordan tables, Wigner-

D

matrices, or e3nn calls. On rMD17, CliffordSTF raises aggregate force-cosine similarity from

0.055

(base Clifford) to

0.551

, an order-of-magnitude relative directional gain, alongside improved magnitude accuracy (force MAE

15.8\%

lower; energy MAE

10.9\%

lower). It outperforms all CG-free or body-ordered baselines in our study (all

\leq 0.17

). On catalysis benchmarks, CliffordSTF achieves the best out-of-distribution S2EF energy MAE on OC22 in our experiments, and the best in-distribution energy MAE among

L \geq 2

methods on OC22 IS2RE. An eleven-variant ablation shows the two tracks are complementary: neither alone matches the combined model.

Can Polat, Erchin Serpedin, Mustafa Kurban +1

Dept. of Electrical & Computer Eng. Texas A&M Univ. College Station, TX, USA · Dept. of Prosthetics & Orthotics College of Science & Eng. Ankara Univ., Ankara, Turkey · Hamad Bin Khalifa Univ. and Texas A&M Univ. at Qatar Doha, Qatar

Machine Learning Interatomic Potentials Equivariant GNNs

Jun 23, 2026physics.chem-ph

ConSolv: Solvent-Conditional Machine Learning Implicit Solvent Potential

Implicit solvent machine learning potentials (MLPs) offer a powerful route to bridging the gap between accuracy and efficiency in molecular simulations. However, existing models have largely focused on aqueous environments, overlooking the diverse and important roles of non-aqueous solvents in areas such as organic synthesis and battery technology. Here, we present ConSolv, a solvent-conditional MLP architecture that explicitly incorporates solvent effects on solute interactions through an attention-based solvent-embedding block. By combining experimental solvation free energy data with ab initio data, we train a single implicit solvent MLP that is transferable across 66 common organic solvents. ConSolv outperforms classical explicit solvent methods and selected ab initio implicit solvent approaches across multiple solvation free energy benchmarks, and demonstrates generalization to unseen solvents. Beyond solvation free energies, the model shows close agreement with experimental nuclear magnetic resonance (NMR) data for

γ

-fluorohydrin molecules in chloroform. ConSolv's architecture is readily extensible to broader chemical spaces and alternative training strategies, while its attention-based design supports explainable artificial intelligence (AI) analysis that can help elucidate complex, solvent-dependent molecular interactions.

Linying Zhang, Julija Zavadlav

Multiscale Modeling of Fluid Materials, Department of Engineering Physics and Computation, TUM School of Engineering and Design, Technical University of Munich, Germany · Atomistic Modeling Center (AMC), Munich Data Science Institute (MDSI), Technical University of Munich, Germany

Machine Learning Interatomic Potentials Molecular Property Prediction

Jun 17, 2026cs.LG

Robust and Interpretable Adaptation of Equivariant Materials Foundation Models via Sparsity-promoting Fine-tuning

Pre-trained materials foundation models, or machine learning interatomic potentials, leverage general physicochemical knowledge to effectively approximate potential energy surfaces. However, they often require domain-specific calibration due to physicochemical diversity as well as mismatches between practical computational settings and those used in constructing the pre-training data. To address this, we propose a sparsity-promoting fine-tuning method that selectively updates model parameters by exploiting the structural properties of E(3)-equivariant materials foundation models. On energy and force prediction tasks across molecular and crystalline benchmarks, our method matches or surpasses full fine-tuning and equivariant low-rank adaptation while updating only

\sim

3~% of parameters, and in some cases as little as

\sim

0.5~%. Beyond energy and force calibration, we further demonstrate task generalizability by applying our method to magnetic moment prediction and magnetism-aware total energy modeling. Finally, analysis of sparsity patterns reveals physically interpretable signatures, such as enhanced

d

-orbital contributions in transition metal systems. Overall, our results establish sparsity-promoting fine-tuning as a flexible and interpretable method for domain specialization of equivariant materials foundation models.

Youngwoo Cho, Seunghoon Yi, Wooil Yang +6

KAIST · Seoul National Univ. · KIAS +2

Machine Learning Interatomic Potentials Equivariant Neural Networks Materials Property Prediction Sparse Fine-Tuning Parameter-Efficient Fine-Tuning

Jun 14, 2026cs.LG

Scalar-pathway fidelity improves physical accuracy in short-range equivariant interatomic potentials

Accurate interatomic potentials enable molecular dynamics of materials, molecules, and interfaces beyond density-functional-theory length and time scales. Equivariant neural network potentials have improved the representation of local geometry. However, their deployable energy surfaces ultimately manifest through invariant scalar channels, whose aggregation and spectral resolution remain comparatively underexamined. Here we use Physics-Aware Neighborhood (PAN) pooling and Physics-Guided Spectral (PGS) mixers as controlled scalar-pathway probes: lightweight, symmetry-preserving modifications that act only on

\ell=0

channels while leaving the equivariant tensor backbone unchanged. Using MACE as a high-body-order mechanistic scaffold, PAN adds coordination-sensitive amplitude modulation, whereas PGS augments edge and readout scalar features with radial and tapered spectral bases. Across metallic Ag, covalent Si, a short-range ionic LiF/Li--F subset, and MD17/rMD17 molecules, this scalar-pathway correction reduces MACE force errors by 22--27% and energy errors by 19--22%; on systems with stress labels, stress errors decrease by 27--28%, at approximately 5% additional inference-FLOPs cost. Directionally consistent gains in Allegro and NequIP further indicate that the correction is portable across distinct short-range equivariant backbones, although effect sizes remain architecture-dependent. These results identify scalar-pathway fidelity as a practical design dimension for short-range equivariant interatomic potentials.

Jia Bi, Alin Marin Elena, Samuel Pinilla

Science and Technology Facilities Council, Harwell Campus, Didcot, OX11 0QX, Oxfordshire, United Kingdom. · Science and Technology Facilities Council, Keckwick Lane, Daresbury, WA4 4AD, Cheshire, United Kingdom. · Diamond Light Source, Harwell Science and Innovation Campus,2026 Didcot, OX11 0QX, Oxfordshire, United Kingdom.

Machine Learning Interatomic Potentials Equivariant GNNs Computational Materials Science

Jun 12, 2026physics.comp-ph

Distilling latent electrostatics from foundation machine learning interatomic potentials

Foundation machine learning interatomic potentials (MLIPs) have enabled atomistic simulations across broad regions of chemical and materials space, but many remain computationally expensive and lack explicit electrostatics, limiting their use for systems governed by long-range interactions and electrical response. Previously, we introduced Latent Ewald Summation (LES), which learns latent atomic charges and long-range electrostatics from density functional theory (DFT) energy and force labels alone. Here, we use LES to extract electrostatics that are latent in foundation models: energies and forces predicted by a teacher model are used to train a lightweight LES-augmented student MLIP, with optional fine-tuning on additional DFT data. The resulting models reduce computational cost while providing access to Born effective charge tensors, and infrared spectra. We benchmark student models distilled from a broad set of foundation MLIPs, including UMA, MACE, Orb, eSEN, GemNet-OC, PET, and EquiformerV2-based models, against experimental infrared spectra for liquid water, concentrated hydrochloric acid, and the anatase TiO2(101)-water interface. Across these systems, electrostatic response can be extracted from most foundation MLIPs. The benchmark further shows that the underlying DFT level and dataset used to train the teacher model play a larger role than architecture in determining electrostatic and spectroscopic accuracy. For the TiO2-water interface, fine-tuning with a modest amount of higher-level DFT data improves structural and infrared predictions. LES-based distillation therefore provides a practical route for converting foundation MLIPs into efficient, electrically responsive models, while also testing the physical fidelity encoded in foundation models.

Xiaoyu Wang, Bingqing Cheng

Department of Chemistry, UC Berkeley, California 94720, United States · Bakar Institute of Digital Materials for the Planet, UC Berkeley, California 94720, United States · Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, 94720, United States

Machine Learning Interatomic Potentials Materials Property Prediction Knowledge Distillation

Jun 8, 2026cs.LG

Loss-Guided Adaptive Scale Refinement for Molecular Force Prediction

Molecular systems involve interactions across multiple spatial scales, from local coordination and short-range perturbations to long-range electrostatic and solvent-mediated effects. However, most molecular representation learning methods rely on manually predefined scales, and the task-optimal modeling scale may not coincide with these fixed levels. This study introduces a loss-guided adaptive scale refinement framework for molecular force prediction, treating predefined scales as initial anchors and discovering task-effective resolutions through interpolation, routing, differentiable scale updates, and scale pool refinement. Using a NaCl aqueous ionic system as a minimal testbed, this study constructs short-scale and long-range force prediction branches and analyzes their complementarity. Oracle hard routing reduces the overall force MAE from 399.65 to 382.67, while continuous oracle interpolation further reduces it to 380.96. In close-contact regimes with nearest-ion distance below 0.6 nm, the close-contact MAE decreases from 327.22 to 260.51. A minimal scale pool update experiment shows that starting from endpoint anchors {0,1}, loss-guided updates automatically generate intermediate scales and recover most of the continuous oracle performance. The final updated scale pool {0,0.125,0.25,0.375,0.5,0.75,1} achieves an overall MAE of 381.23. These results support adaptive scale refinement as a promising direction for molecular representation learning, especially when fixed-scale modeling is insufficient.

Limin Yu

School of Medical Imaging, Division of Medical Technology, Tianjin Key Laboratory of Functional Imaging, Tianjin Medical University, Tianjin 300203, China

Machine Learning Interatomic Potentials Multi-Scale Feature Fusion Molecular Representation Learning

Jun 6, 2026cond-mat.mtrl-sci

Inverse design of bespoke interatomic potentials via active learning by information-matching

Interatomic potentials (IPs) enable large-scale atomistic simulations beyond the reach of first-principles methods, but their predictive reliability depends critically on the selection of training data, quantified uncertainty, and model expressiveness. Active learning (AL) provides a principled framework for constructing efficient and accurate IPs, yet most strategies reduce parameter uncertainty without explicitly accounting for the specific material properties being predicted. The information-matching (IM) approach addresses this limitation by requiring that the selected training data provide at least as much parameter space information as needed to achieve prescribed uncertainty targets for selected quantities of interest (QoIs). Here, we apply IM to develop bespoke IPs specifically tailored for predicting plastic strength in metals. Due to the high computational cost of simulating plastic strength, we employ an indirect IM strategy that targets inexpensive intermediate QoIs that correlate with strength. The IM method enables precise parameter constraints with minimal training data, yielding precise predictions for both the intermediate QoIs and plastic strength. Yet, model error remains a key limitation, and a post hoc uncertainty inflation correction provides a viable means to mitigate this limitation. These findings illustrate both the promise and limits of uncertainty-aware AL for predicting complex material properties.

Yonatan Kurniawan, Logan D. Williams, Amit Samanta +6

Department of Physics and Astronomy, Brigham Young University, Provo, UT, USA · Department of Physics and Astronomy, Brigham Young University, Provo, UT, USA. · Lawrence Livermore National Laboratory, Livermore, CA, USA +7

Uncertainty Quantification Machine Learning Interatomic Potentials Active Learning Materials Property Prediction

Jun 2, 2026cs.LG

Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials

Machine learning interatomic potentials (MLIPs) enable efficient and accurate atomistic simulations but depend critically on the quality and diversity of the training data. We introduce Stein kernelized molecular dynamics (SKMD), an enhanced sampling method that uses interacting particle dynamics to acquire informative training configurations for the active learning and fine-tuning of MLIPs. SKMD corresponds to a stochastic variant of Stein variational gradient descent that is adapted for molecular dynamics by incorporating asynchronous particle updates and a kernel of global atomic descriptors, which provides a symmetry-aware measure of configurational similarity. Unlike other enhanced samplers used in molecular dynamics, SKMD preserves the Boltzmann distribution as the asymptotic distribution of the dynamics. This property enforces a balance between the exploration of diverse configurations and attraction toward high-probability regions of the energy landscape. We further propose an approach to efficient online data acquisition using an adaptive stopping criterion that selects non-redundant training data over the course of simulation. We demonstrate SKMD for the active learning of a neural network model of the Müller-Brown potential and the fine-tuning of a MACE interatomic potential for alanine dipeptide. Compared to active learning baselines, our method achieves higher model accuracy in fewer training iterations with the same number of acquired training samples.

Joanna Zou, Fraser Birks, Dallas Foster +1

Center for Computational Science & Engineering, Schwarzman College of Computing, MIT · Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick · NVIDIA

Machine Learning Interatomic Potentials Active Learning Adaptive Sampling Kernel Methods Molecular Dynamics Simulation Stein Variational Gradient Descent