DEQuify your force field: More efficient simulations using deep equilibrium models

2025/09/10 by Andreas Burger, Burger, Andreas, Luca Thiede +4 · 1 citation
Materials Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Model Reduction and Neural Networks #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2509.08734

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Machine learning force fields show great promise in enabling more accurate molecular dynamics simulations compared to manually derived ones. Much of the progress in recent years was driven by exploiting prior knowledge about physical systems, in particular symmetries under rotation, translation, and reflections. In this paper, we argue that there is another important piece of prior information that, thus fa,r hasn't been explored: Simulating a molecular system is necessarily continuous, and successive states are therefore extremely similar. Our contribution is to show that we can exploit this information by recasting a state-of-the-art equivariant base model as a deep equilibrium model. This allows us to recycle intermediate neural network features from previous time steps, enabling us to improve both accuracy and speed by 10%-20% on the MD17, MD22, and OC20 200k datasets, compared to the non-DEQ base model. The training is also much more memory efficient, allowing us to train more expressive models on larger systems.

Citations

• One-Step Diffusion Distillation via Deep Equilibrium Models
• Deep Equilibrium Diffusion Restoration with Parallel Sampling
• Lightweight equivariant model for efficient machine learning interatomic potentials
• TorchDEQ: A Library for Deep Equilibrium Models
• From Molecules to Materials: Pre-training Large Generalizable Models for Atomic Property Prediction
• EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations
• Long-Short-Range Message-Passing: A Physics-Informed Framework to Capture Non-Local Interaction for Scalable Molecular Dynamics Simulation
• Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs
• ViSNet: an equivariant geometry-enhanced graph neural network with vector-scalar interactive message passing for molecules
• Accurate global machine learning force fields for molecules with hundreds of atoms
• Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs
• MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields
• Deep Equilibrium Optical Flow Estimation
• Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics
• On Training Implicit Models
• Stabilizing Equilibrium Models by Jacobian Regularization
• GemNet: Universal Directional Graph Neural Networks for Molecules
• How Attentive are Graph Attention Networks?
• JFB: Jacobian-Free Backpropagation for Implicit Networks
• Spherical Message Passing for 3D Graph Networks
• Equivariant message passing for the prediction of tensorial properties and molecular spectra
• E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
• Directional Message Passing for Molecular Graphs
• Deep Equilibrium Models
• Cormorant: Covariant Molecular Neural Networks
• Trellis Networks for Sequence Modeling
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• A Theoretically Grounded Application of Dropout in Recurrent Neural Networks

Cited by

• Shoot from the HIP: Hessian Interatomic Potentials without derivatives

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