# Solving Newton's Equations of Motion with Large Timesteps using Recurrent Neural Networks based Operators

arXiv: https://arxiv.org/abs/2004.06493 · HTML: https://mlsanity.com/paper/2004.06493/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2020.

## Built on by (most cited first, 6 of 6)

- [Exact conservation laws for neural network integrators of dynamical systems](https://mlsanity.com/paper/2209.11661/) (2022)
- [Force-Free Molecular Dynamics Through Autoregressive Equivariant Networks](https://mlsanity.com/paper/2503.23794/) (2025)
- [FlashMD: long-stride, universal prediction of molecular dynamics](https://mlsanity.com/paper/2505.19350/) (2025)
- [Locally-symplectic neural networks for learning volume-preserving dynamics](https://mlsanity.com/paper/2109.09151/) (2021)
- [Neural DAEs: Constrained neural networks](https://mlsanity.com/paper/2211.14302/) (2022)
- [Machine learning for advancing low-temperature plasma modeling and simulation](https://mlsanity.com/paper/2307.00131/) (2023)

## Abstract (arXiv)

Classical molecular dynamics simulations are based on solving Newton's equations of motion. Using a small timestep, numerical integrators such as Verlet generate trajectories of particles as solutions to Newton's equations. We introduce operators derived using recurrent neural networks that accurately solve Newton's equations utilizing sequences of past trajectory data, and produce energy-conserving dynamics of particles using timesteps up to 4000 times larger compared to the Verlet timestep. We demonstrate significant speedup in many example problems including 3D systems of up to 16 particles.