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Tsinghua-BIMSA Computational & Applied Mathematics (CAM) Seminar
Numerical methods for Mean field Games based on Gaussian Processes and Fourier Features
Numerical methods for Mean field Games based on Gaussian Processes and Fourier Features
Organizers
Jie Du
, Computational & Applied Mathematics Group
, Hui Yu
Speaker
Xianjin Yang
Time
Thursday, April 28, 2022 2:00 PM - 3:00 PM
Venue
1110
Online
Tencent 408 2490 3761
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Abstract
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.