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

TL;DR

This paper introduces a machine learning approach to simulate long-time dynamics in molecular systems by learning structure-preserving maps, improving efficiency and accuracy over traditional methods.

Contribution

The authors develop a data-driven, structure-preserving ML method that learns the mechanical action to generate accurate long-time molecular dynamics trajectories.

Findings

Eliminates artifacts of non-structure-preserving ML models

Enables transferability across thermodynamic conditions and compositions

Can be iteratively applied as a correction method

Abstract

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.