A parameterized Wasserstein Hamiltonian flow approach for solving the Schrödinger equation
Hao Wu, Shu Liu, Xiaojing Ye, Haomin Zhou
Publications
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Simulation of Wasserstein geometric flows from a generative approach
Parameterized Wasserstein gradient flow
Yijie Jin, Shu Liu, Hao Wu, Xiaojing Ye, Haomin Zhou
Numerical Analysis on Neural Network projected schemes for approximating one dimensional Wasserstein Gradient Flows
Xinzhe Zuo, Jiaxi Zhao, Shu Liu, Stanley Osher, Wuchen Li
Parametrized Wasserstein Hamiltonian flow
Hao Wu, Shu Liu, Xiaojing Ye, Haomin Zhou
Neural parametric Fokker-Planck equations
Shu Liu, Wuchen Li, Hongyuan Zha, Haomin Zhou
Primal-Dual algorithm for numerical PDEs with preconditioning
A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations
Shu Liu, Stanley Osher, Wuchen Li
A first-order computational method for Reaction-Diffusion type equations via Primal-Dual Hybrid Gradient method
Shu Liu, Siting Liu, Stanley Osher, Wuchen Li
Numerical analysis of a first-order computational algorithm for reaction-diffusion equations via the primal-dual hybrid gradient method
Shu Liu, Xinzhe Zuo, Stanley Osher, Wuchen Li
Computational methods related to optimal transport & Hamilton-Jacobi equation
Neural Hamilton-Jacobi Characteristic Flows for Optimal Transport
Yesom Park, Shu Liu, Mo Zhou, Stanley Osher
A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling
Jianbo Cui, Shu Liu, Haomin Zhou
Neural Monge Map estimation and its applications.
Jiaojiao Fan∗, Shu Liu∗, Shaojun Ma, Haomin Zhou, Yongxin Chen
A particle-evolving method for approximating the optimal transport plan
Shu Liu∗, Haodong Sun∗, Hongyuan Zha
Learning high dimensional Wasserstein geodesics
Shu Liu∗, Shaojun Ma∗, Yongxin Chen, Hongyuan Zha, Haomin Zhou
Control & Sampling on discrete sets
Accelerated Markov Chain Monte Carlo Algorithms on Discrete States
Bohan Zhou, Shu Liu, Xinzhe Zuo, Wuchen Li
Optimal Control for Stochastic Nonlinear Schrödinger Equation on Graph
Jianbo Cui, Shu Liu, Haomin Zhou
Wasserstein Hamiltonian flow with common noise on graph.
Jianbo Cui, Shu Liu, Haomin Zhou
What is a stochastic Hamiltonian process on finite graph? An optimal transport answer
Jianbo Cui, Shu Liu, Haomin Zhou