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. Built on this result, we propose to solve the MVEs by
minimizing this potential function, while utilizing the neural networks for
function approximation. We validate the empirical performance of our approach
by comparing with state-of-the-art NN-based PDE solvers on several example
problems.Comment: Accepted to NeurIPS 202