Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations

arXiv cs.LG Papers
machine-learning force-fields molecular-dynamics graph-neural-networks efficiency arxiv

Summary

Introduces implicit machine learning force fields (I-MLFFs) that replace deep neural network stacks with fixed-point equations, enabling warm-starting and up to 5x compute/memory savings across graph neural network architectures for molecular dynamics simulations.

arXiv:2607.29158v1 Announce Type: new 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.
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# Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations
Source: [https://arxiv.org/abs/2607.29158](https://arxiv.org/abs/2607.29158)
[View PDF](https://arxiv.org/pdf/2607.29158)

> 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\.

## Submission history

From: Johannes Maeß \[[view email](https://arxiv.org/show-email/07274e77/2607.29158)\] **\[v1\]**Fri, 31 Jul 2026 08:38:13 UTC \(19,180 KB\)

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