Learning gradient flows via fluctuating hydrodynamics from particles

The aim is to learn gradient flow evolution from underlying particle models. Specifically, we will discuss how the mobility and the evolution operator of suitable diffusive processes can be learned from particle data. As rigorous result, error estimates for the mobility associated with the simple exclusion process are presented. Methodologically, fluctuating hydrodynamics, seen as "thermodynamically correct" stochastic perturbation of a deterministic gradient flow, will play a central role.