Efficient Langevin sampling with position-dependent diffusion

TL;DR

This paper presents a second-order accurate numerical method for Langevin sampling with position-dependent diffusion, improving efficiency while maintaining accuracy in sampling the invariant measure.

Contribution

The paper introduces a novel numerical scheme for Brownian dynamics with position-dependent diffusion that requires only one force evaluation per timestep and achieves second-order accuracy.

Findings

Numerical experiments confirm the second-order convergence.

The method efficiently samples the invariant measure.

Analysis of sampling bias using exotic aromatic Butcher-series.

Abstract

We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring only one force evaluation per timestep. Analysis of the sampling bias is performed using the algebraic framework of exotic aromatic Butcher-series. Numerical experiments confirm the theoretical order of convergence and illustrate the efficiency of the new method.