20 citations · 44 across the 6 of their papers we have counts for
7 papers
Forward-backward algorithm for functions with locally Lipschitz gradient: applications to mean field games
Luis M. Briceno-Arias, Francisco José Silva, Xianjin Yang
In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable…
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…
Two-scale homogenization of a stationary mean-field game
Rita Ferreira, Diogo Gomes, Xianjin Yang
In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically osci…
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.…
Existence of positive solutions for an approximation of stationary mean-field games
Nojood Almayouf, Elena Bachini, Andreia Chapouto +22
Here, we consider a regularized mean-field game model that features a low-order regularization. We prove the existence of solutions with positive density. To do so, we combine a pr…