Gilles Vilmart: High-order sampling of the invariant distribution of ergodic stochastic dynamics: preconditioning […]

Speaker
Gilles Vilmart, Univ. of Geneva

Abstract
Preconditioning techniques for ergodic stochastic dynamics are attractive to enhance the convergence to the invariant measure especially in high dimension (or infinite dimension for SPDEs), to tackle the issues of stiffness and multi-modal target distributions. Achieving high order of accuracy is however challenging in the context. In this talk, we present an integrator for overdamped Langevin dynamics with position dependent diffusion tensor, with a postprocessor that 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. This talk is based on joint work with Eugen Bronasco (Univ. Geneva), Benedict Leimkuhler, and Dominic Phillips (Univ. Edinburgh). Preprints and papers available at: https://www.unige.ch/~vilmart