A patch that imparts unconditional stability to explicit integrators for Langevin-like equations

Nawaf Bou-Rabee, Eric Vanden-Eijnden

Abstract: This paper extends the results in [8] to stochastic differential equations (SDEs) arising in molecular dynamics. It implements a patch to explicit integrators that consists of a Metropolis–Hastings step. The ‘patched integrator’ preserves the SDE’s equilibrium distribution and is accurate on finite time intervals. As a corollary this paper proves the integrator’s accuracy in estimating finite-time dynamics along an infinitely long solution - a first in molecular dynamics. The paper also covers multiple time-steps, holonomic constraints and scalability. Finally, the paper provides numerical tests supporting the theory.