10 papers
Semi-Lagrangian Approximation of Master Equations with Individual Noise on Finite Graphs
Jianbo Cui, Tonghe Dang
We develop and analyze a fully discrete semi-Lagrangian method for vector master equations associated with mean field games (MFGs) with individual noise on finite graphs. The metho…
Convergence and variational structure of a staggered scheme for mean field games with individual noise on graphs
Jianbo Cui, Tonghe Dang
We propose and analyze a time-staggered numerical scheme for mean field game (MFG) systems with individual noise on finite graphs. Numerically solving such coupled forward--backwar…
First-Order Convergence of Monotone Schemes for Hamilton--Jacobi Equations on the Wasserstein Space on Graphs
Jianbo Cui, Tonghe Dang
We prove first-order convergence of semi-discrete monotone finite difference schemes for Hamilton--Jacobi equations on the Wasserstein space over a finite graph. A central challeng…
Newton's method for optimal transport problem on graphs
Qujiangxue Chen, Jianbo Cui, Luca Dieci +1
In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and veloc…
Quantifying the effect of graph structure on strong Feller property of SPDEs
Jianbo Cui, Tonghe Dang, Jialin Hong +1
This paper investigates how the structure of the underlying graph influences the behavior of stochastic partial differential equations (SPDEs) on finite tree graphs, where each edg…
Hamilton--Jacobi--Bellman equation for optimal control of stochastic Wasserstein--Hamiltonian system on graphs
Jianbo Cui, Tonghe Dang
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-base…
Stoch-IDENT: New Method and Mathematical Analysis for Identifying SPDEs from Data
Jianbo Cui, Roy Y. He
In this paper, we propose Stoch-IDENT, a novel framework for identifying stochastic partial differential equations (SPDEs) from observational data. Our method can handle linear and…
Finite difference schemes for Hamilton--Jacobi equation on Wasserstein space on graphs
Jianbo Cui, Tonghe Dang, Chenchen Mou
This work proposes and studies numerical schemes for initial value problems of Hamilton--Jacobi equations (HJEs) with a graph individual noise on the Wasserstein space on graphs. N…
A Wong--Zakai resonance-based integrator for nonlinear Schrödinger equation with white noise dispersion
Jianbo Cui, Georg Maierhofer
We introduce a novel approach to numerical approximation of nonlinear Schrödinger equation with white noise dispersion in the regime of low-regularity solutions. Approximating such…
A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling
Jianbo Cui, Shu Liu, Haomin Zhou
We propose a supervised learning scheme for the first order Hamilton--Jacobi PDEs in high dimensions. The scheme is designed by using the geometric structure of Wasserstein Hamilto…