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.

1. Renato Spacek, Gabriel Stoltz, Extending the regime of linear response with synthetic forcings, 2023 [arXiv:2303.03551] [hal-04019027]

2. Jose Antonio Carrillo, Franca Hoffmann, Andrew M. Stuart, Urbain Vaes, The Ensemble Kalman Filter in the Near-Gaussian Setting, 2022 [arXiv:2212.13239] [hal-03913934]

3. Gabriel Stoltz, Error estimates and variance reduction for nonequilibrium stochastic dynamics, 2022 [arXiv:2211.10717] [hal-03864796]

4. Mouad Ramil, Tony Lelièvre, Julien Reygner, Mathematical foundations for the Parallel Replica algorithm applied to the underdamped Langevin dynamics. MRS Communications, Cambridge University Press, 2022 [10.1557/s43579-022-00207-3] [hal-03747075]

5. Grigorios A. Pavliotis, Gabriel Stoltz, Urbain Vaes, Mobility estimation for Langevin dynamics using control variates, 2022 [arXiv:2206.09781] [hal-03701412]

6.  Roberta Flenghi, Benjamin Jourdain, Central limit theorem over non-linear functionals of empirical measures: beyond the iid setting, 2022 [arXiv:2204] [hal-03653469]

7. Gabriel Stoltz, Computational statistical physics and hypocoercivity, 2021 [arXiv:2112.08221] [hal-03482498]

8.  Petr Plechac, Gabriel Stoltz and Ting Wang, Martingale product estimators for sensitivity analysis in computational statistical physics, 2021 [arXiv:2112.00126] [hal-03462697]

FORTHCOMING / ONGOING

Past

• Summer School: ``Sampling high-dimensional probability measures: applications in (non)equilibrium molecular dynamics and statistics'', CERMICS, Marne la Vallée, September 25-29, 2023

• Minisymposium Numerical methods in statistical physics (organised by Alessandra Iacobucci and Gabriel Stoltz) at the 14th International Conference on Monte Carlo Methods and Applications, June 26-30, 2023, Sorbonne University 

• Journée SINEQ, INRIA, Paris, Decembre 15th, 2022

• SINEQ Kick-off meeting, INRIA, Paris, December 8th, 2021