Machine Learning Interatomic Potentials

Machine-learning interatomic potentials (MLIPs) have enabled molecular dynamics at near ab initio accuracy, yet remain limited to energies and forces by construction, leaving electronic observables such as dipole moments and polarizabilities inaccessible. We introduce DenSNet, a density-first approach to machine-learned electronic structure that learns the Hohenberg--Kohn map from nuclear configurations to the ground-state electron density. Our approach employs an SE(3)-equivariant neural network to predict density coefficients of a flexible atom-centered Gaussian basis, combined with a $Δ$-learning strategy that uses superposed atomic densities as a prior to accelerate training. A second equivariant network then maps the predicted density to the total energy, providing a unified framework for molecular dynamics and electronic structure. We validate DenSNet on ethanol, ethanethiol, and resorcinol, where infrared spectra from machine-learned trajectories show excellent agreement with experimental gas-phase measurements. To test scalability, we train on polythiophene oligomers with 1--6 monomers and extrapolate to chains of up to 12 monomers, generating stable long-time trajectories whose infrared spectra agree with reference density functional theory calculations. Here, we show that reinstating the electron density as the central learned quantity opens a practical route to transferable prediction of spectroscopic and electronic observables in large-scale molecular simulations.

Glassy silica is a foundational material in optics and electronics, yet accurately predicting its medium-range order (MRO) remains a major challenge for machine-learning interatomic potentials (MLIPs). While local MLIPs reproduce the short-range SiO4 tetrahedral network well, it remains unclear whether locality alone is sufficient to recover the first sharp diffraction peak (FSDP), the principal experimental signature of MRO. Here, we combine neutron and X-ray diffraction measurements with large-scale molecular dynamics driven by two MACE-based models: a short-range (SR) potential and a long-range (LR) extension incorporating reciprocal-space gated attention. The SR model systematically over-structures the network, producing an overly intense FSDP in both the liquid and glassy states. Incorporating long-range interactions improves agreement with experiment for the liquid structure by reducing this excess ordering, but the LR model still fails to recover the experimental amorphous MRO after quenching. Ring-statistics and bond-angle analyses reveal that SR model exhibits an artificially narrow distribution dominated by six-membered rings, while the LR model produces a broader but still biased ring population. Despite preserving the correct tetrahedral geometry, both models show limited variability in Si-O-Si angles, indicating constrained network flexibility. These structural signatures demonstrate that both models retain excessive memory of the parent liquid network, leading to kinetically trapped and nonphysical medium-range configurations during vitrification. These results show that explicit long-range interactions are necessary but not sufficient for predictive modelling of disordered silica and suggest that accurate MRO further requires training data and sampling strategies that adequately represent the liquid-to-glass transition.

Universal Machine Learning Interatomic Potentials (uMLIPs), pre-trained on massively diverse datasets encompassing inorganic materials and organic molecules across the entire periodic table, serve as foundational models for quantum-accurate physical simulations. However, uMLIP training requires second-order derivatives, which lack corresponding parallel training frameworks; moreover, scaling to the billion-parameter regime causes explosive growth in computation and communication overhead, making its training a tremendous challenge. We introduce MatRIS-MoE, a billion-parameter Mixture-of-Experts model built upon invariant architecture, and {Janus}, a pioneering high-dimensional distributed training framework for uMLIPs with hardware-aware optimizations. Deployed across two Exascale supercomputers, our code attains a peak performance of 1.2/1.0 EFLOPS (24%/{35.5%} of theoretical peak) in single precision at over 90% parallel efficiency, compressing the training of billion-parameter uMLIPs from weeks to hours. This work establishes a new high-water mark for AI-for-Science (AI4S) foundation models at Exascale and provides essential infrastructure for rapid scientific discovery.

We present an exascale workflow for materials discovery using atomistic graph foundation models built on HydraGNN. We jointly train on 16 open first-principles datasets (544+ million structures covering 85+ elements) using a multi-task architecture with per-dataset heads and a scalable ADIOS2/DDStore data pipeline. On Frontier, we execute six large-scale DeepHyper hyperparameter optimization campaigns in FP64 and promote the top-performing message-passing models to sustained 2,048-node training, yielding a PaiNN-based lead model. The resulting model enables billion-scale screening, evaluating 1.1 billion atomistic structures in 50 seconds, compressing a workload that would require years of first-principles computation, and supports data-scarce fine-tuning across diverse downstream tasks. We quantify precision-performance tradeoffs (BF16/FP32/FP64), demonstrate transfer across twelve chemically diverse downstream tasks, and establish seamless strong- and weak-scaling across Frontier, Aurora, and Perlmutter. This work allows fast and reliable exploration of vast chemical design spaces that are otherwise inaccessible to first-principles methods.

We present an open Molecular Crystal (MC) database of Machine-Learned Interatomic Potentials (MLIP) called MolCryst-MLIPs. The first release comprises fine-tuned MACE models for nine molecular crystal systems---Benzamide, Benzoic acid, Coumarin, Durene, Isonicotinamide, Nicotinic acid , Niacinamide, Pyrazinamide, and Resorcinol---developed using the Automated Machine Learning Pipeline (AMLP), which streamlines the entire MLIP development workflow, from reference data generation to model training and validation, into a reproducible and user-friendly pipeline. Models are fine-tuned from the MACE-MH-1 foundation model omol head), yielding a mean energy MAE of 0.141 kJ/mol/atom and a mean force MAE of 0.648 kJ/mol/Angstrom across all systems. Benchmarked against three state-of-the-art foundation models on the DFT-labelled polymorph set, only the fine-tuned models resolve the polymorphic energy landscape. Dynamical stability and structural integrity, as assessed through energy conservation, P2 orientational order parameters, and radial distribution functions, are evaluated using molecular dynamics simulations. The released models and datasets constitute a growing open database of validated MLIPs, ready for production MD simulations of molecular crystal polymorphism across the polymorphic landscape of each target compound under different thermodynamic conditions.

Accurate prediction of energy and forces for 3D molecular systems is one of fundamental challenges at the core of AI for Science applications. Many powerful and data-efficient neural networks predict molecular energies and forces from single atomic configurations. However, one crucial aspect of the data generation process is rarely considered while learning these models i.e. Molecular Dynamics (MD) simulation. MD simulations generate time-ordered trajectories of atomic positions that fluctuate in energy and explore regions of the potential energy surface (e.g., under standard NVE/NVT ensembles), rather than being constructed to steadily lower the potential energy toward a minimum as in geometry relaxations. This work explores a novel way to leverage MD data, when available, to improve the performance of such predictors. We introduce a novel training strategy called FRAMES, that use an auxiliary loss function for exploiting the temporal relationships within MD trajectories. Counter-intuitively, on two atomistic benchmarks and a synthetic system we observe that minimal temporal information, captured by pairs of just two consecutive frames, is often sufficient to obtain the best performance, while adding longer trajectory sequences can introduce redundancy and degrade performance. On the widely used MD17 and ISO17 benchmarks, FRAMES significantly outperforms its Equiformer baseline, achieving highly competitive results in both energy and force accuracy. Our work not only presents a novel training strategy which improves the accuracy of the model, but also provides evidence that for distilling physical priors of atomic systems, more temporal data is not always better.

Mechanistic understanding and rational design of complex chemical systems depend on fast and accurate predictions of electronic structures beyond individual building blocks. However, if the system exceeds hundreds of atoms, first-principles quantum mechanical (QM) modeling becomes impractical. In this study, we developed FB-GNN-MBE by integrating a fragment-based graph neural network (FB-GNN) into the many-body expansion (MBE) theory and demonstrated its capacity to reproduce first-principles potential energy surfaces (PES) for hierarchically structured systems with manageable accuracy, complexity, and interpretability. Specifically, we divided the entire system into basic building blocks (fragments), evaluated their one-fragment energies using a QM model, and addressed many-fragment interactions using the structure-property relationships trained by FB-GNNs. Our investigation shows that FB-GNN-MBE achieves chemical accuracy in predicting two-body (2B) and three-body (3B) energies across water, phenol, and mixture benchmarks, as well as the one-dimensional dissociation curves of water and phenol dimers. To transfer the success of FB-GNN-MBE across various systems with minimal computational costs and data demands, we developed and validated a teacher-student learning protocol. A heavy-weight FB-GNN trained on a mixed-density water cluster ensemble (teacher) distills its learned knowledge and passes it to a light-weight GNN (student), which is later fine-tuned on a uniform-density (H2O)21 cluster ensemble. This transfer learning strategy resulted in efficient and accurate prediction of 2B and 3B energies for variously sized water clusters without retraining. Our transferable FB-GNN-MBE framework outperformed conventional non-FB-GNN-based models and provided a scalable and accurate route toward interaction energies of large molecular assemblies.

As $SE(3)$-equivariant graph neural networks mature as a core tool for 3D atomistic modeling, improving their efficiency, expressivity, and physical consistency has become a central challenge for large-scale applications. In this work, we introduce EquiformerV3, the third generation of the $SE(3)$-equivariant graph attention Transformer, designed to advance all three dimensions: efficiency, expressivity, and generality. Building on EquiformerV2, we have the following three key advances. First, we optimize the software implementation, achieving $1.75\times$ speedup. Second, we introduce simple and effective modifications to EquiformerV2, including equivariant merged layer normalization, improved feedforward network hyper-parameters, and attention with smooth radius cutoff. Third, we propose SwiGLU-$S^2$ activations to incorporate many-body interactions for better theoretical expressivity and to preserve strict equivariance while reducing the complexity of sampling $S^2$ grids. Together, SwiGLU-$S^2$ activations and smooth-cutoff attention enable accurate modeling of smoothly varying potential energy surfaces (PES), generalizing EquiformerV3 to tasks requiring energy-conserving simulations and higher-order derivatives of PES. With these improvements, EquiformerV3 trained with the auxiliary task of denoising non-equilibrium structures (DeNS) achieves state-of-the-art results on OC20, OMat24, and Matbench Discovery.

GROMACS is a de-facto standard for classical Molecular Dynamics (MD). The rise of AI-driven interatomic potentials that pursue near-quantum accuracy at MD throughput now poses a significant challenge: embedding neural-network inference into multi-GPU simulations retaining high-performance. In this work, we integrate the MLIP framework DeePMD-kit into GROMACS, enabling domain-decomposed, GPU-accelerated inference across multi-node systems. We extend the GROMACS NNPot interface with a DeePMD backend, and we introduce a domain decomposition layer decoupled from the main simulation. The inference is executed concurrently on all processes, with two MPI collectives used each step to broadcast coordinates and to aggregate and redistribute forces. We train an in-house DPA-1 model (1.6 M parameters) on a dataset of solvated protein fragments. We validate the implementation on a small protein system, then we benchmark the GROMACS-DeePMD integration with a 15,668 atom protein on NVIDIA A100 and AMD MI250x GPUs up to 32 devices. Strong-scaling efficiency reaches 66% at 16 devices and 40% at 32; weak-scaling efficiency is 80% to 16 devices and reaches 48% (MI250x) and 40% (A100) at 32 devices. Profiling with the ROCm System profiler shows that >90% of the wall time is spent in DeePMD inference, while MPI collectives contribute <10%, primarily since they act as a global synchronization point. The principal bottlenecks are the irreducible ghost-atom cost set by the cutoff radius, confirmed by a simple throughput model, and load imbalance across ranks. These results demonstrate that production MD with near ab initio fidelity is feasible at scale in GROMACS.

The demand for safe, high-energy-density batteries has spotlighted halide solid-state electrolytes, which offer the potential for enhanced ionic mobility, electrochemical stability, and interfacial deformability. Accelerating their discovery requires extensive molecular dynamics, which has been increasingly enabled by universal machine learning interatomic potentials trained on foundational datasets. However, the dynamic softness of halides poses a stringent test of whether general-purpose models can reliably replace first-principles calculations under the highly distorted, elevated-temperature regimes necessary to probe ion transport. Here, we present AQVolt26, a dataset of 322,656 r$^2$SCAN single-point calculations for lithium halides, generated via high-temperature configurational sampling across $\sim$5K structures. We demonstrate that foundational datasets provide a strong baseline for stable halide chemistries and transfer local forces well, however absolute energy predictions degrade in distorted higher-temperature regimes. Co-training with AQVolt26 resolves this blind spot. Furthermore, incorporating Materials Project relaxation data improves near-equilibrium performance but degrades extreme-strain robustness without enhancing high-temperature force accuracy. These results demonstrate that domain-specific configurational sampling is essential for the reliable dynamic screening of halide electrolytes. Furthermore, our findings suggest that while foundational models provide a robust base, they are most effective for dynamically soft solid-state chemistries when augmented with targeted, high-temperature data. Finally, we show that near-equilibrium relaxation data serves as a task-specific complement rather than a universally beneficial addition.

Local curvature of potential energy surfaces is critical for predicting certain experimental observables of molecules and materials from first principles, yet it remains far beyond reach for complex systems. In this work, we introduce a Hessian-informed Machine Learning Interatomic Potential (Hi-MLIP) that captures such curvature reliably, thereby enabling accurate analysis of associated thermodynamic and kinetic phenomena. To make Hessian supervision practically viable, we develop a highly efficient training protocol, termed Hessian INformed Training (HINT), achieving two to four orders of magnitude reduction for the requirement of expensive Hessian labels. HINT integrates critical techniques, including Hessian pre-training, configuration sampling, curriculum learning and stochastic projection Hessian loss. Enabled by HINT, Hi-MLIP significantly improves transition-state search and brings Gibbs free-energy predictions close to chemical accuracy especially in data-scarce regimes. Our framework also enables accurate treatment of strongly anharmonic hydrides, reproducing phonon renormalization and superconducting critical temperatures in close agreement with experiment while bypassing the computational bottleneck of anharmonic calculations. These results establish a practical route to enhancing curvature awareness of machine learning interatomic potentials, bridging simulation and experimental observables across a wide range of systems.

Machine-learned interatomic potentials (MLIPs), particularly graph neural network (GNN)-based models, offer a promising route to achieving near-density functional theory (DFT) accuracy at significantly reduced computational cost. However, their practical deployment is often limited by the large volumes of expensive quantum mechanical training data required. In this work, we introduce a transfer learning framework, Transfer-PaiNN (T-PaiNN), that substantially improves the data efficiency of GNN-MLIPs by leveraging inexpensive classical force field data. The approach consists of pretraining a PaiNN MLIP architecture on large-scale datasets generated from classical molecular simulations, followed by fine-tuning (dubbed autotuning) using a comparatively small DFT dataset. We demonstrate the effectiveness of autotuning T-PaiNN on both gas-phase molecular systems (QM9 dataset) and condensed-phase liquid water. Across all cases, T-PaiNN significantly outperforms models trained solely on DFT data, achieving order-of-magnitude reductions in mean absolute error while accelerating training convergence. For example, using the QM9 data set, error reductions of up to 25 times are observed in low-data regimes, while liquid water simulations show improved predictions of energies, forces, and experimentally relevant properties such as density and diffusion. These gains arise from the model's ability to learn general features of the potential energy surface from extensive classical sampling, which are subsequently refined to quantum accuracy. Overall, this work establishes transfer learning from classical force fields as a practical and computationally efficient strategy for developing high-accuracy, data-efficient GNN interatomic potentials, enabling broader application of MLIPs to complex chemical systems.

The core of molecular dynamics simulation fundamentally lies in the interatomic potential. Traditional empirical potentials lack accuracy, while first-principles methods are computationally prohibitive. Machine learning interatomic potentials (MLIPs) promise near-quantum accuracy at linear cost, but existing models still face challenges in efficiency and stability. We presents Machine Learning Advances Neural Network (MLANet), an efficient and robust graph neural network framework. MLANet introduces a dual-path dynamic attention mechanism for geometry-aware message passing and a multi-perspective pooling strategy to construct comprehensive system representations. This design enables highly accurate modeling of atomic environments while achieving exceptional computational efficiency, making high-fidelity simulations more accessible. Tested across a wide range of datasets spanning diverse systems, including organic molecules (e.g., QM7, MD17), periodic inorganic materials (e.g., Li-containing crystals), two-dimensional materials (e.g., bilayer graphene, black phosphorus), surface catalytic reactions (e.g., formate decomposition), and charged systems, MLANet maintains competitive prediction accuracy while its computational cost is markedly lower than mainstream equivariant models, and it enables stable long-time molecular dynamics simulations. MLANet provides an efficient and practical tool for large-scale, high-accuracy atomic simulations.

The development of machine learning interatomic potentials faces a critical computational bottleneck with the generation and labeling of useful training datasets. We present a novel application of determinantal point processes (DPPs) to the task of selecting informative subsets of atomic configurations to label with reference energies and forces from costly quantum mechanical methods. Through experiments with hafnium oxide data, we show that DPPs are competitive with existing approaches to constructing compact but diverse training sets by utilizing kernels of molecular descriptors, leading to improved accuracy and robustness in machine learning representations of molecular systems. Our work identifies promising directions to employ DPPs for unsupervised training data curation with heterogeneous or multimodal data, or in online active learning schemes for iterative data augmentation during molecular dynamics simulation.

Accurate atomistic simulations of gas-surface scattering require potential energy surfaces that remain reliable over broad configurational and energetic ranges while retaining the efficiency needed for extensive trajectory sampling. Here, we develop a data-driven workflow for constructing a machine-learning interatomic potential (MLIP) tailored to gas-surface scattering dynamics, using nitric oxide (NO) scattering from highly oriented pyrolytic graphite (HOPG) as a benchmark system. Starting from an initial ab initio molecular dynamics (AIMD) dataset, local atomic environments are described by SOAP descriptors and analyzed in a reduced feature space obtained through principal component analysis. Farthest point sampling is then used to build a compact training set, and the resulting Deep Potential model is refined through a query-by-committee active-learning strategy using additional configurations extracted from molecular dynamics simulations over extended ranges of incident energies and surface temperatures. The final MLIP reproduces reference energies and forces with high fidelity and enables large-scale molecular dynamics simulations of NO scattering from graphite at a computational cost far below that of AIMD. The simulations provide detailed insight into adsorption energetics, trapping versus direct scattering probabilities, translational energy loss, angular distributions, and rotational excitation. Overall, the results reproduce the main experimental trends and demonstrate that descriptor-guided sampling combined with active learning offers an efficient and transferable strategy for constructing MLIPs for gas-surface interactions.

Long-range electrostatic and polarization interactions play a central role in molecular and condensed-phase systems, yet remain fundamentally incompatible with locality-based machine-learning interatomic potentials. Although modern SO(3)-equivariant neural potentials achieve high accuracy for short-range chemistry, they cannot represent the anisotropic, slowly decaying multipolar correlations governing realistic materials, while existing long-range extensions either break SO(3) equivariance or fail to maintain energy-force consistency. Here we introduce EquiEwald, a unified neural interatomic potential that embeds an Ewald-inspired reciprocal-space formulation within an irreducible SO(3)-equivariant framework. By performing equivariant message passing in reciprocal space through learned equivariant k-space filters and an equivariant inverse transform, EquiEwald captures anisotropic, tensorial long-range correlations without sacrificing physical consistency. Across periodic and aperiodic benchmarks, EquiEwald captures long-range electrostatic behavior consistent with ab initio reference data and consistently improves energy and force accuracy, data efficiency, and long-range extrapolation. These results establish EquiEwald as a physically principled paradigm for long-range-capable machine-learning interatomic potentials.

Machine learning interatomic potentials (MLIPs) have become widely used tools in atomistic simulations. For much of the history of this field, the most commonly employed architectures were based on short-ranged atomic energy contributions, and the assumption of locality still persists in many modern foundation models. While this approach has enabled efficient and accurate modelling for many use cases, it poses intrinsic limitations for systems where long-range electrostatics, charge transfer, or induced polarization play a central role. A growing body of work has proposed extensions that incorporate electrostatic effects, ranging from locally predicted atomic charges to self-consistent models. While these models have demonstrated success for specific examples, their underlying assumptions, and fundamental limitations are not yet well understood. In this work, we present a framework for treating electrostatics in MLIPs by viewing existing models as coarse-grained approximations to density functional theory (DFT). This perspective makes explicit the approximations involved, clarifies the physical meaning of the learned quantities, and reveals connections and equivalences between several previously proposed models. Using this formalism, we identify key design choices that define a broader design space of self-consistent electrostatic MLIPs. We implement salient points in this space using the MACE architecture and a shared representation of the charge density, enabling controlled comparisons between different approaches. Finally, we evaluate these models on two instructive test cases: metal-water interfaces, which probe the contrasting electrostatic response of conducting and insulating systems, and charged vacancies in silicon dioxide. Our results highlight the limitations of existing approaches and demonstrate how more expressive self-consistent models are needed to resolve failures.

Machine-learned interatomic potentials (MLIPs) are deployed for high-throughput materials screening without formal reliability guarantees. We show that a single MLIP used as a stability filter misses 93% of density functional theory (DFT)-stable materials (recall 0.07) on a 25,000-material benchmark. Proof-Carrying Materials (PCM) closes this gap through three stages: adversarial falsification across compositional space, bootstrap envelope refinement with 95% confidence intervals, and Lean 4 formal certification. Auditing CHGNet, TensorNet and MACE reveals architecture-specific blind spots with near-zero pairwise error correlations (r <= 0.13; n = 5,000), confirmed by independent Quantum ESPRESSO validation (20/20 converged; median DFT/CHGNet force ratio 12x). A risk model trained on PCM-discovered features predicts failures on unseen materials (AUC-ROC = 0.938 +/- 0.004) and transfers across architectures (cross-MLIP AUC-ROC ~ 0.70; feature importance r = 0.877). In a thermoelectric screening case study, PCM-audited protocols discover 62 additional stable materials missed by single-MLIP screening - a 25% improvement in discovery yield.

We introduce Flexible Cutoff Learning (FCL), a method for training machine learning interatomic potentials (MLIPs) whose cutoff radii can be adjusted after training. Unlike conventional MLIPs that fix the cutoff radius during training, FCL models are trained by randomly sampling cutoff radii independently for each atom. The resulting model can then be deployed with different per-atom cutoff radii depending on the application, enabling application-specific optimization of the accuracy-cost tradeoff. Using a differentiable cost model, these per-atom cutoffs can be optimized for specific target systems after training. We demonstrate FCL with a modified MACE architecture trained on the MAD dataset. For a subset featuring molecular crystals, optimized per-atom cutoffs reduce computational cost by more than 60% while increasing force errors by less than 1%. These results show that FCL enables training of a single general-purpose MLIP that can be adapted to diverse applications through post-training cutoff optimization, eliminating the need for retraining.

Machine Learning Interatomic Potentials (MLIPs) enable accurate large-scale atomistic simulations, yet improving their expressive capacity efficiently remains challenging. Here we systematically investigate Mixture-of-Experts (MoE) and Mixture-of-Linear-Experts (MoLE) architectures within the DPA3 framework for MLIPs and analyze the effects of routing strategies and expert designs. We show that sparse activation combined with shared experts yields substantial performance gains, and that nonlinear MoE formulations outperform MoLE when shared experts are present, underscoring the importance of nonlinear expert specialization. Furthermore, element-wise routing consistently surpasses configuration-level routing, while global MoE routing often leads to numerical instability. The resulting element-wise MoE model consistently outperforms all DPA3-based baselines across the OMol25, OMat24, and OC20M benchmarks. Analysis of routing patterns reveals chemically interpretable expert specialization aligned with periodic-table trends, indicating that the model effectively captures element-specific chemical characteristics for precise interatomic modeling.

Machine-learning interatomic potentials (MLIPs) have advanced rapidly, with many top models relying on strong physics-based inductive biases. However, as models scale to larger systems like biomolecules and electrolytes, they struggle to accurately capture long-range (LR) interactions, leading current approaches to rely on explicit physics-based terms or components. In this work, we propose AllScAIP, a straightforward, attention-based, and energy-conserving MLIP model that scales to O(100 million) training samples. It addresses the long-range challenge using an all-to-all node attention component that is data-driven. Extensive ablations reveal that in low-data/small-model regimes, inductive biases improve sample efficiency. However, as data and model size scale, these benefits diminish or even reverse, while all-to-all attention remains critical for capturing LR interactions. Our model achieves state-of-the-art energy/force accuracy on molecular systems, as well as a number of physics-based evaluations (OMol25), while being competitive on materials (OMat24) and catalysts (OC20). Furthermore, it enables stable, long-timescale MD simulations that accurately recover experimental observables, including density and heat of vaporization predictions.

The Hessian matrix (second derivatives) encodes far richer local curvature of the potential energy surface than energies and forces alone. However, training machine-learning interatomic potentials (MLIPs) with full Hessians is often impractical because explicitly forming and storing Hessian matrices scales quadratically in cost and memory. We introduce Projected Hessian Learning (PHL), a scalable second-order training framework that injects curvature information using only Hessian-vector products (HVPs). Rather than constructing the Hessian, PHL projects curvature along stochastic probe directions and uses an unbiased stochastic trace-based loss with favorable system-size scaling, enabling curvature-informed training without quadratic memory growth. We benchmark PHL on a chemically diverse dataset of reactants, products, transition states, intrinsic reaction coordinates, and normal-mode sampled geometries computed at omegaB97XD/6-31G(d). We compare energy-force training (E-F), two HVP-based schemes (E-F-HVP with one-hot or randomized probes), and full energy-force-Hessian training (E-F-H). With randomized probes per minibatch, both HVP schemes match full-Hessian training in energy, force, and Hessian accuracy while delivering >24x epoch speedups for the small molecular systems studied. In a fixed-probe regime with one HVP per molecule, randomized projections consistently outperform one-column probing, especially for far-from-equilibrium geometries. Overall, PHL replaces explicit Hessian supervision with force-complexity curvature training, retaining most second-order accuracy gains while scaling to larger, more complex molecular systems.

Foundation MLIPs demonstrate broad applicability across diverse material systems and have emerged as a powerful and transformative paradigm in chemical and computational materials science. Equivariant MLIPs achieve state-of-the-art accuracy in a wide range of benchmarks by incorporating equivariant inductive bias. However, the reliance on tensor products and high-degree representations makes them computationally costly. This raises a fundamental question: as quantum mechanical-based datasets continue to expand, can we develop a more compact model to thoroughly exploit high-dimensional atomic interactions? In this work, we present MatRIS (Materials Representation and Interaction Simulation), an invariant MLIP that introduces attention-based modeling of three-body interactions. MatRIS leverages a novel separable attention mechanism with linear complexity $O(N)$, enabling both scalability and expressiveness. MatRIS delivers accuracy comparable to that of leading equivariant models on a wide range of popular benchmarks (Matbench-Discovery, MatPES, MDR phonon, Molecular dataset, etc). Taking Matbench-Discovery as an example, MatRIS achieves an F1 score of up to 0.847 and attains comparable accuracy at a lower training cost. The work indicates that our carefully designed invariant models can match or exceed the accuracy of equivariant models at a fraction of the cost, shedding light on the development of accurate and efficient MLIPs.

Van der Waals (vdW) interactions are essential for describing molecules and materials, from drug design and catalysis to battery applications. These omnipresent interactions must also be accurately included in machine-learned force fields. The many-body dispersion (MBD) method stands out as one of the most accurate and transferable approaches to capture vdW interactions, requiring only atomic $C_6$ coefficients and polarizabilities as input. We present MBD-ML, a pretrained message passing neural network that predicts these atomic properties directly from atomic structures. Through seamless integration with libMBD, our method enables the immediate calculation of MBD-inclusive total energies, forces, and stress tensors. By eliminating the need for intermediate electronic structure calculations, MBD-ML offers a practical and streamlined tool that simplifies the incorporation of state-of-the-art vdW interactions into any electronic structure code, as well as empirical and machine-learned force fields.

Accurate modelling of electrostatic interactions and charge transfer is fundamental to computational chemistry, yet most machine learning interatomic potentials (MLIPs) rely on local atomic descriptors that cannot capture long-range electrostatic effects. We present a new electrostatic foundation model for molecular chemistry that extends the MACE architecture with explicit treatment of long-range interactions and electrostatic induction. Our approach combines local many-body geometric features with a non-self-consistent field formalism that updates learnable charge and spin densities through polarisable iterations to model induction, followed by global charge equilibration via learnable Fukui functions to control total charge and total spin. This design enables an accurate and physical description of systems with varying charge and spin states while maintaining computational efficiency. Trained on the OMol25 dataset of 100 million hybrid DFT calculations, our models achieve chemical accuracy across diverse benchmarks, with accuracy competitive with hybrid DFT on thermochemistry, reaction barriers, conformational energies, and transition metal complexes. Notably, we demonstrate that the inclusion of long-range electrostatics leads to a large improvement in the description of non-covalent interactions and supramolecular complexes over non-electrostatic models, including sub-kcal/mol prediction of molecular crystal formation energy in the X23-DMC dataset and a fourfold improvement over short-ranged models on protein-ligand interactions. The model's ability to handle variable charge and spin states, respond to external fields, provide interpretable spin-resolved charge densities, and maintain accuracy from small molecules to protein-ligand complexes positions it as a versatile tool for computational molecular chemistry and drug discovery.

Allegro is a machine learning interatomic potential model designed to predict atomic properties in molecules using E(3) equivariant neural networks. When training this model, there tends to be a trade-off between accuracy and inference time. For this reason, we apply multi-objective hyperparameter optimization to both objectives. Additionally, we experiment with modified architectures by constructing variants of Allegro: one extended with additional classical layers and one incorporating quantum-classical hybrid layers. We evaluate all models on QM9, rMD17-aspirin, rMD17-benzene, and a self-generated dataset of copper-lithium structures. As results, both variants surpass Allegro in force prediction accuracy across multiple datasets. The classical variant consistently improves over the baseline, while the quantum-classical hybrid variant achieves the best overall force prediction accuracy on the Cu-Li dataset, where it was fully optimized, outperforming the classical variant by approximately 13%. Notably, the hybrid variant also achieves competitive results on the remaining datasets despite using hyperparameters transferred from Cu-Li without dataset-specific optimization, suggesting that quantum-classical hybridization is a promising direction for enhancing MLIP architectures.

Following our previous work (J. Phys. Chem. Lett., 2026, 17, 5, 1288-1295), we propose the DMTS-NC approach, a distilled multi-time-step (DMTS) strategy using non-conservative (NC) forces to further accelerate atomistic molecular dynamics simulations using foundation neural network models such as FeNNix-Bio1. There, a dual-level reversible reference system propagator algorithm (RESPA) formalism couples a target accurate conservative potential to a simplified distilled representation optimized for the production of non-conservative forces. Despite being non-conservative, the distilled architecture is designed to enforce key physical priors, such as equivariance under rotation and cancellation of atomic force components. These choices facilitate the distillation process and therefore improve drastically the robustness of simulation, significantly limiting abnormal discrepancies between the two models, thus achieving excellent agreement with the forces data. Overall, the DMTS-NC scheme is found to be more stable and efficient than its conservative counterpart with additional speedups reaching 15-30% over DMTS. Requiring no fine-tuning steps, it is easier to implement and can be pushed to the limit of the systems physical resonances to maintain accuracy while providing maximum efficiency. We obtain additional speedup by combining hydrogen mass repartitioning (HMR), High Hydrogen Friction (HHF) to further extended the largest timestep up to 10fs of our schemes while conserving stability and accuracy. As for DMTS, DMTS-NC is applicable to any neural network potential and can be applied to approaches that are computationally heavier than FeNNix-Bio1. We show a proof of principle applying the approach to the distillation of MACE-OFF23 with consequent speedups ranging from 3.66 to 5.64 compared to single timestep.

We introduce AceFF, a pre-trained machine learning interatomic potential (MLIP) optimized for small molecule drug discovery. While MLIPs have emerged as efficient alternatives to Density Functional Theory (DFT), generalizability across diverse chemical spaces remains difficult. AceFF addresses this by refining the TensorNet2 architecture and training it on a comprehensive dataset of drug-like compounds. This approach yields a force field that balances high-throughput inference speed with DFT-level accuracy. We introduce two models sharing the same architecture: \mbox{AceFF-2}, trained on our own dataset of small molecules and supporting the essential medicinal chemistry elements (H, B, C, N, O, F, Si, P, S, Cl, Br, I); and \mbox{AceFF-2-OMOL}, trained on a subset of OMol25 containing the AceFF-2 elements plus the common biomolecular ion elements Na and K. The models are explicitly trained to handle charged states. Validation against rigorous benchmarks, including complex torsional energy scans, molecular dynamics trajectories, batched minimizations, and tests of force and energy accuracy, demonstrates that AceFF is state-of-the-art for organic molecules in the accuracy and speed regime important for drug discovery. The AceFF-2 and AceFF-2-OMol model weights and inference code are available at https://huggingface.co/Acellera/AceFF-2.0 and https://huggingface.co/Acellera/AceFF-2-OMOL.

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, oversquashing, 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 22% reduction in force and a roughly 40 percent reduction in energy prediction error relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.

Fundamental tasks in computational chemistry, from transition state search to vibrational analysis, rely on molecular Hessians, which are the second derivatives of the potential energy. Yet, Hessians are computationally expensive to calculate and scale poorly with system size, with both quantum mechanical methods and neural networks. In this work, we demonstrate that Hessians can be predicted directly from a deep learning model, without relying on automatic differentiation or finite differences. We observe that one can construct SE(3)-equivariant, symmetric Hessians from irreducible representations (irrep) features up to degree $l$=2 computed during message passing in graph neural networks. This makes HIP Hessians one to two orders of magnitude faster, more accurate, more memory efficient, easier to train, and enables more favorable scaling with system size. We validate our predictions across a wide range of downstream tasks, demonstrating consistently superior performance for transition state search, accelerated geometry optimization, zero-point energy corrections, and vibrational analysis benchmarks. We open-source the HIP codebase and model weights to enable further development of the direct prediction of Hessians at https://github.com/BurgerAndreas/hip