- 计算和应用数学讨论班

Numerical methods for Mean field Games based on Gaussian Processes and Fourier Features

组织者

杜洁 , Computational & Applied Mathematics Group , 蔚辉

演讲者

杨先津

时间

2022年04月28日 14:00 至 15:00

地点

1110

线上

Tencent 408 2490 3761 ()

摘要

In this talk, I will present two numerical methods, the Gaussian Process (GP) method and the Fourier Features (FF) algorithm, to solve mean field games (MFGs). The GP algorithm approximates the solution of a MFG with maximum a posteriori probability estimators of GPs conditioned on the partial differential equation (PDE) system of the MFG at a finite number of sample points. To improve the performance, we introduce the FF method, whose insight comes from the recent trend of approximating positive definite kernels with random Fourier features. We give the existence and the convergence proofs for both algorithms. We show the efficacy of our algorithms through experiments on a stationary MFG with a non-local coupling and on a time-dependent planning problem.