This work introduces implicit machine learning force fields, which replace explicit stacks of neural network layers with self-consistent fixed-point equations, and demonstrates this across three major classes of graph neural networks: invariant, equivariant Cartesian tensor, and SO(3)-equivariant spherical-tensor architectures.
Abstract
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.
We present AquaGen, the first all-atom, explicit solvent, periodic-boundary-condition-aware generative model that produces molecular configurations from the Boltzmann distribution at a fraction of the cost of molecular dynamics (MD). This is in contrast with existing generative models that remove degrees of freedom by operating on coarse-grained, vacuum, or implicit solvent systems. Operating at this resolution allows for post-processing through force field energy evaluations and MD simulations, and enables the prediction of relevant properties in a gray-box manner (as ensemble averages of potential energy evaluations over generated samples). We demonstrate the utility of this paradigm on absolute hydration free energy (AHFE), producing estimates 4-10x faster and with comparable accuracy to standard GPU-based MD. By generating uncorrelated samples from alchemical Boltzmann distributions, we create more accurate, interpretable, and refinable ensemble predictions with calibrated uncertainty estimates, unlike regression methods which are entirely black-box predictors. Our approach also yields predictable benefits from increasing train- and test-time compute, realized by scaling model size and generating more samples, respectively. We believe that this approach demonstrates the utility of high-resolution ensemble generation for free energy estimation, with future potential to replace MD in tasks such as the prediction of lipophilicity, membrane permeability, or absolute binding free energy (ABFE) -- whose grounding and interpretability may be critical for the development of new drugs and materials.
Emmanuel Bengio, Sanjeev Raja, Y. Pang et al.· 1 citation
Molecular dynamics (MD) is essential for investigating atomic‐scale processes in materials and molecular systems, but the cost of high‐accuracy machine learning force field simulations still limits accessible system sizes and timescales. Here, we propose a practical model‐switching strategy for Deep Potential (DP)‐based MD simulations that alternates between independently trained DP models with different cutoff radii: a standard 6 Å model for higher accuracy and a reduced‐cutoff 4 Å model for faster inference. The method was implemented in LAMMPS/DeePMD and evaluated using solid‐phase anatase TiO
2
and liquid‐phase polyethylene glycol (PEG). For anatase TiO
2
, the 1:3 4–6 Å switching scheme preserved radial distribution function (RDF) correlations of 0.996 or higher relative to the 6 Å baseline while achieving a 1.24‐fold speedup. For PEG, the switching scheme maintained RDF correlations of 0.996 or higher with a 1.18‐fold speedup. Additional optimization using network‐size reduction and mixed‐precision inference achieved a 2.53‐fold speedup with RDF correlations of 0.975–0.988. Constant particle‐number, pressure, and temperature (NPT) simulations remained stable, whereas constant particle‐number, volume, and energy (NVE) simulations revealed system‐dependent energy‐drift behavior, particularly for aggressively optimized models. These results demonstrate that DP model switching provides a simple and practical route for accelerating structural MD simulations while highlighting the need for validation when strict energy conservation is required.
Ryuya Kanda, Megumu Yamazaki, Yuta Yoshimoto et al.· Advanced Intelligent Discove...· 0 citations
AI2Pot is presented, a scalable and unified MLIP framework that seamlessly integrates model training, evaluation, and large-scale MD simulations with PyTorch-compatible ecosystem, and offers an user-friendly end-to-end framework for the developing, training, and deploying MLIPs for large scale MD.
Hanyu Liu, Linggang Zhu, Xuanguang Zhang et al.· 0 citations
The Active Learning Framework (ALF), an open-source Python package designed to streamline the design and deployment of MLIP training datasets on High Performance Computing resources, is introduced, illustrating ALF’s effectiveness in compiling datasets that capture essential chemical and structural regimes.
V. Grizzi, P. Lohr, Nikita Fedik et al.· Journal of Chemical Theory a...· 0 citations
Foundation machine learning interatomic potentials (MLIPs) are increasingly being used as drop-in replacements for first-principles calculations, enabling simulations of materials at length and time scales that were previously inaccessible. However, due to lack of ground truth data, their accuracy on structural and dynamical observables in finite thermodynamic ensembles is yet to be established. Here, we introduce Dyna-Mat-v1.0, a benchmark dataset of condensed-phase first-principles molecular dynamics trajectories designed to test foundation MLIPs at realistic finite-temperature conditions. Using this dataset, we evaluate 15 foundation MLIPs across four model tiers by comparing both single-point energy and force errors on first-principles configurations and observables generated from MLIP-driven trajectories. We find that"on average"models with lower single-point force errors also yield lower errors for structural and dynamical observables. However, there are individual systems for which low force errors lead to qualitative failures in the predicted structure. Pressure remains poorly described across most models, pointing to limitations in the density functional theory stress labels available in current large-scale training datasets. Finally, we construct an accuracy-cost Pareto frontier to identify the best trade-offs for molecular dynamics with foundation MLIPs, finding that the latest generation of cross-trained models is close to Pareto-optimal according to the accuracy metrics considered here. Overall, Dyna-Mat-v1.0 shows that end-to-end finite-temperature validation is essential for quantifying the predictive behaviour of foundation MLIPs, and provides a simple, scalable route for assessing them beyond static and harmonic benchmarks relevant to materials design.
Mikołaj J Gawkowski, Nongnuch Artrith, Silvia Bonfanti et al.· 1 citation
UniFlow is introduced, the first scalable generative model that unifies protein ensemble generation and machine-learned coarse-grained force fields for molecular dynamics simulation within a single framework, and paves the way for a unified class of models that bridges generative ensemble modeling with physics-based molecular simulation.
Yikai Liu, Ming Chen, Guang Lin· bioRxiv· 0 citations