Special Session 168: Stochastic Analysis and Large Scale Interacting Systems

From particles via fluctuating hydrodynamics to gradient flows: Rigorous error estimates
Johannes Zimmer
TU Munich
Germany
Co-Author(s):    Nicolas Dirr and Zhengyan Wu
Abstract:
The aim is to learn gradient flow evolution from underlying particle models. Specifically, we will discuss how the mobility of the thermodynamic evolution operator of suitable diffusive processes can be learned from particle data. Results will consider the case where the evolution is of Wasserstein gradient flow type. The central tool is a stochastic partial differential equation of fluctuating hydrodynamics type, which will be introduced in the talk. As rigorous result, error estimates for the mobility associated with the simple exclusion process are presented. Methodologically, this approach relies on the fact that fluctuating hydrodynamics can be seen as thermodynamically correct stochastic perturbation of a deterministic gradient flow.