2 citations · 2 across the 8 of their papers we have counts for
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Parameterized Methods for Game Dynamics
Yijie Jin, Haomin Zhou
We introduce a parameterized computational framework for the evolution of strategic behavior in continuous games. We consider the collective dynamics of players through a time-depe…
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…
Discrete Mean Field Games on Finite Graphs as Initial Value Optimization
Yaxin Feng, Yang Xiang, Haomin Zhou
In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph M…
Computing the Gross-Pitaevskii Ground State via Wasserstein Gradient Flow in Diffeomorphism Space
Xiangxiong Zhang, Haomin Zhou
We compute the ground state of the Gross--Pitaevskii equation (GPE) via Wasserstein gradient descent in diffeomorphism space. We represent the density as the push-forwa…
Deep Tangent Bundle (DTB) method: a Deep Neural Network approach to compute solutions of PDES
Hao Wu, Haomin Zhou
We develop a numerical framework, the Deep Tangent Bundle (DTB) method, that is suitable for computing solutions of evolutionary partial differential equations (PDEs) in high dimen…
A parameterized Wasserstein Hamiltonian flow approach for solving the Schrödinger equation
Hao Wu, Shu Liu, Xiaojing Ye +1
In this paper, we propose a new method to compute the solution of time-dependent Schrödinger equation (TDSE). Using push-forward maps and Wasserstein Hamiltonian flow, we reformula…
Parameterized Wasserstein Gradient Flow
Yijie Jin, Shu Liu, Hao Wu +2
We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduc…
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…