# Learning Interatomic Potentials at Multiple Scales

arXiv: https://arxiv.org/abs/2310.13756 · HTML: https://mlsanity.com/paper/2310.13756/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 55 references that are in the map.
- First posted on arXiv 20 Oct 2023.

## Builds on (most cited first, 19 of 19)

- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [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)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [TorchMD: A deep learning framework for molecular simulations](https://mlsanity.com/paper/2012.12106/) (2020)
- [Ewald-based Long-Range Message Passing for Molecular Graphs](https://mlsanity.com/paper/2303.04791/) (2023)
- [Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size](https://mlsanity.com/paper/2304.10061/) (2023)
- [Allegro-Legato: Scalable, Fast, and Robust Neural-Network Quantum Molecular Dynamics via Sharpness-Aware Minimization](https://mlsanity.com/paper/2303.08169/) (2023)

## Built on by (most cited first, 5 of 5)

- [Force-Free Molecular Dynamics Through Autoregressive Equivariant Networks](https://mlsanity.com/paper/2503.23794/) (2025)
- [Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics](https://mlsanity.com/paper/2402.06275/) (2024)
- [Faster Molecular Dynamics with Neural Network Potentials via Distilled Multiple Time-Stepping and Non-Conservative Forces](https://mlsanity.com/paper/2602.14975/) (2026)
- [Speculative Sampling For Faster Molecular Dynamics](https://mlsanity.com/paper/2606.02455/) (2026)
- [Multi-objective optimization and quantum hybridization of equivariant deep learning interatomic potentials](https://mlsanity.com/paper/2602.16908/) (2026)

## Abstract (arXiv)

The need to use a short time step is a key limit on the speed of molecular dynamics (MD) simulations. Simulations governed by classical potentials are often accelerated by using a multiple-time-step (MTS) integrator that evaluates certain potential energy terms that vary more slowly than others less frequently. This approach is enabled by the simple but limiting analytic forms of classical potentials. Machine learning interatomic potentials (MLIPs), in particular recent equivariant neural networks, are much more broadly applicable than classical potentials and can faithfully reproduce the expensive but accurate reference electronic structure calculations used to train them. They still, however, require the use of a single short time step, as they lack the inherent term-by-term scale separation of classical potentials. This work introduces a method to learn a scale separation in complex interatomic interactions by co-training two MLIPs. Initially, a small and efficient model is trained to reproduce short-time-scale interactions. Subsequently, a large and expressive model is trained jointly to capture the remaining interactions not captured by the small model. When running MD, the MTS integrator then evaluates the smaller model for every time step and the larger model less frequently, accelerating simulation. Compared to a conventionally trained MLIP, our approach can achieve a significant speedup (~3x in our experiments) without a loss of accuracy on the potential energy or simulation-derived quantities.