20 citations · 44 across the 6 of their papers we have counts for
4 papers · 1 filter
A Mini-Batch Method for Solving Nonlinear PDEs with Gaussian Processes
Xianjin Yang, Houman Owhadi
Gaussian processes (GPs) based methods for solving partial differential equations (PDEs) demonstrate great promise by bridging the gap between the theoretical rigor of traditional…
Sparse Gaussian processes for solving nonlinear PDEs
Rui Meng, Xianjin Yang
This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs)…
Numerical methods for Mean field Games based on Gaussian Processes and Fourier Features
Chenchen Mou, Xianjin Yang, Chao Zhou
In this article, we propose two numerical methods, the Gaussian Process (GP) method and the Fourier Features (FF) algorithm, to solve mean field games (MFGs). The GP algorithm appr…
The Hessian Riemannian flow and Newton's method for Effective Hamiltonians and Mather measures
Diogo A. Gomes, Xianjin Yang
Effective Hamiltonians arise in several problems, including homogenization of Hamilton--Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry--Mather theory.…