中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：Zhenfu Wang ( Peking University)
题 目：Entropy-Dissipation Informed Neural Networks for McKean-Vlasov type PDEs
时 间：2023.04.11（星期二）16:00-17:00
地 点：数学院南楼N213
摘 要：We extend the concept of self-consistency for the Fokker-Planck equation (FPE) [Shen et al., 2022] 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.
附件：