Adaptive multi-stage integrators for optimal energy conservation in molecular simulations

TL;DR

The paper presents an Adaptive Integration Approach (AIA) that automatically selects optimal numerical integrators for molecular simulations, significantly improving energy conservation and sampling efficiency over traditional methods.

Contribution

Introduction of AIA, a method that adaptively chooses the best integrator scheme for molecular simulations to enhance energy conservation and efficiency.

Findings

AIA outperforms standard Verlet and fixed integrators in energy conservation.

AIA achieves up to 5 times better sampling efficiency.

The method is effective in both molecular dynamics and hybrid Monte Carlo simulations.

Abstract

We introduce a new Adaptive Integration Approach (AIA) to be used in a wide range of molecular simulations. Given a simulation problem and a step size, the method automatically chooses the optimal scheme out of an available family of numerical integrators. Although we focus on two-stage splitting integrators, the idea may be used with more general families. In each instance, the system-specific integrating scheme identified by our approach is optimal in the sense that it provides the best conservation of energy for harmonic forces. The AIA method has been implemented in the BCAM-modified GROMACS software package. Numerical tests in molecular dynamics and hybrid Monte Carlo simulations of constrained and unconstrained physical systems show that the method successfully realises the fail-safe strategy. In all experiments, and for each of the criteria employed, the AIA is at least as good as, and often significantly outperforms the standard Verlet scheme, as well as fixed parameter, optimized two-stage integrators. In particular, the sampling efficiency found in simulations using the AIA is up to 5 times better than the one achieved with other tested schemes.