报告题目 (Title)：基于得分的输运建模用于均场Fokker-Planck方程

报告人 (Speaker)：吴悦 博士 (香港科技大学数学系)

报告时间 (Time)：2023年10月18日（周三） 9:00

报告地点 (Place)：腾讯会议（742224079）

邀请人(Inviter)：秦晓雪

主办部门：理学院数学系

报告摘要：We use the score-based transport modeling method to solve the mean-field Fokker-Planck equations, which we call MSBTM. We establish an upper bound on the time derivative of the Kullback-Leibler (KL) divergence to MSBTM numerical estimation from the exact solution, thus validates the MSBTM approach. Besides, we provide an error analysis for the algorithm. In numerical experiments, we study three types of mean-field Fokker-Planck equation and their corresponding dynamics of particles in interacting systems. The MSBTM algorithm is numerically validated through qualitative and quantitative comparison between the MSBTM solutions, the results of integrating the associated stochastic differential equation and the analytical solutions if available.