8 papers
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…
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…
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…
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…
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…