ANR "SINEQ"

SImulating NonEQuilibrium stochastic dynamics

2022 - 2025

This project is supported by the Agence Nationale de la Recherche (grant ANR-21-CE40-0006)

Scientific aim: Computing equilibrium properties in computational statistical physics can be performed efficiently using various variance reduction techniques. On the other hand, the simulation of nonequilibrium properties remains limited by the space-time scales which can be achieved by brute force numerical methods. In particular, the estimators of transport coefficients obtained from the linear response of steady-state averages of nonequilibrium stochastic dynamics are plagued by very large variances and/or biases. The aim of this project is to provide new tools for the mathematical and numerical analysis of nonequilibrium stochastic dynamics. The techniques employed lie at the interface of various subfields of mathematics, ranging from probability theory and the study of stochastic processes to functional analysis and the theory of partial differential equations; with an emphasis on the numerical analysis of Monte Carlo methods and time discretization of stochastic differential equations.

Keywords: probability, numerical analysis, partial differential equations, molecular dynamics, Monte Carlo methods, variance reduction methods.