# Learning the action for long-time-step simulations of molecular dynamics

arXiv: https://arxiv.org/abs/2508.01068 · HTML: https://mlsanity.com/paper/2508.01068/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 1 Aug 2025.

## Builds on (most cited first, 8 of 8)

- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps](https://mlsanity.com/paper/2103.05632/) (2021)
- [Symplectic Gaussian Process Regression of Hamiltonian Flow Maps](https://mlsanity.com/paper/2009.05569/) (2020)
- [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)
- [Learning Large-Time-Step Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2111.15176/) (2021)
- [Artificial Intelligence for Direct Prediction of Molecular Dynamics Across Chemical Space](https://mlsanity.com/paper/2505.16301/) (2025)

## Built on by (most cited first, 2 of 2)

- [Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics](https://mlsanity.com/paper/2601.22123/) (2026)
- [Generative Modeling of Stochastic Dynamics for Long-Time Evolution](https://mlsanity.com/paper/2610.00546/) (2026)

## Abstract (arXiv)

The equations of classical mechanics can be used to model the time evolution of countless physical systems, from the astrophysical to the atomic scale. Accurate numerical integration requires small time steps, which limits the computational efficiency -- especially in cases such as molecular dynamics that span wildly different time scales. Using machine-learning (ML) algorithms to predict trajectories allows one to greatly extend the integration time step, at the cost of introducing artifacts such as lack of energy conservation and loss of equipartition between different degrees of freedom of a system. We propose learning data-driven structure-preserving (symplectic and time-reversible) maps to generate long time-step classical dynamics and show that this method is equivalent to learning the mechanical action of the system of interest. These models can be learned based on short reference trajectories, and be transferred across thermodynamic conditions and chemical composition. We show that an action-derived ML integrator eliminates the pathological behavior of non-structure-preserving ML predictors, and that the method can be applied iteratively, serving as a correction to computationally cheaper direct predictors.