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

arXiv: https://arxiv.org/abs/2509.08734 · HTML: https://mlsanity.com/paper/2509.08734/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 47 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [Deep Equilibrium Optical Flow Estimation](https://mlsanity.com/paper/2204.08442/) (2022)
- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [Trellis Networks for Sequence Modeling](https://mlsanity.com/paper/1810.06682/) (2018)
- [From Molecules to Materials: Pre-training Large Generalizable Models for Atomic Property Prediction](https://mlsanity.com/paper/2310.16802/) (2023)
- [TorchDEQ: A Library for Deep Equilibrium Models](https://mlsanity.com/paper/2310.18605/) (2023)
- [Deep Equilibrium Diffusion Restoration with Parallel Sampling](https://mlsanity.com/paper/2311.11600/) (2023)
- [Lightweight equivariant model for efficient machine learning interatomic potentials](https://mlsanity.com/paper/2311.02869/) (2023)

## Built on by (most cited first, 3 of 3)

- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)
- [Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations](https://mlsanity.com/paper/2607.29158/) (2026)
- [Physics-Aligned Electronic Ground-State Learning Improves Generalization](https://mlsanity.com/paper/2610.10298/) (2026)

## Abstract (arXiv)

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.