Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems

TL;DR

This paper introduces a time step rescaling method that improves discrete-time Langevin integrators, enabling them to better replicate continuous-time dynamical properties across equilibrium and nonequilibrium simulations.

Contribution

The authors propose a novel time step rescaling technique that corrects dynamical defects in Langevin integrators, enhancing their accuracy and applicability.

Findings

Time step rescaling improves dynamical accuracy of Langevin integrators.

A specific splitting scheme is identified as broadly suitable for various Langevin simulations.

The method works effectively in equilibrium, nonequilibrium, and path sampling contexts.

Abstract

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently-developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.