Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs

Understand

We extend the concept of self-consistency for the Fokker-Planck equation (FPE) to the more general McKean-Vlasov equation (MVE).

• While FPE describes the macroscopic behavior of particles under drift and diffusion, MVE accounts for the additional inter-particle interactions, which are often highly singular in physical systems.
• Two important examples considered in this paper are the MVE with Coulomb interactions and the vorticity formulation of the 2D Navier-Stokes equation.
• We show that a generalized self-consistency potential controls the KL-divergence between a hypothesis solution to the ground truth, through entropy dissipation.