Parameterized Wasserstein gradient flow
Yijie Jin, Shu Liu, Hao Wu, Xiaojing Ye, Haomin Zhou
Journal of Computational Physics Volume 524, 2025
Paper | Slides
Publications
You can also find my articles on my Google Scholar profile.
Journal Articles
A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations
Shu Liu, Stanley Osher, Wuchen Li
arXiv: 2411.06278. 2024
Paper | SlidesA first-order computational method for Reaction-Diffusion type equations via Primal-Dual Hybrid Gradient method
Shu Liu, Siting Liu, Stanley Osher, Wuchen Li
Journal of Computational Physics Volume 500, 2024
Paper | SlidesNumerical Analysis on Neural Network projected schemes for approximating one dimensional Wasserstein Gradient Flows
Xinzhe Zuo, Jiaxi Zhao, Shu Liu, Stanley Osher, Wuchen Li
arXiv: 2402.16821. 2024
PaperA supervised learning scheme for computing Hamilton-Jacobi equation via density coupling
Jianbo Cui, Shu Liu, Haomin Zhou
arXiv: 2401.15954. 2024
PaperNumerical 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
arXiv: 2401.14602. 2024
Paper | SlidesOptimal Control for Stochastic Nonlinear Schrödinger Equation on Graph
Jianbo Cui, Shu Liu, Haomin Zhou
SIAM Journal on Control and Optimization Vol. 61, Iss. 4 2023.
PaperWasserstein Hamiltonian flow with common noise on graph.
Jianbo Cui, Shu Liu, Haomin Zhou
SIAM Journal on Applied Mathematics, Vol. 83, Iss. 2 pp. 484 - 509, 2023.
PaperParametrized Wasserstein Hamiltonian flow
Hao Wu, Shu Liu, Xiaojing Ye, Haomin Zhou
arXiv: 2306.00191. 2023
Paper | SlidesNeural Monge Map estimation and its applications.
Jiaojiao Fan∗, Shu Liu∗, Shaojun Ma, Haomin Zhou, Yongxin Chen
Transaction on Machine Learning Research [Featured Certification], 2023
Paper | SlidesStochastic Wasserstein Hamiltonian Flows.
Jianbo Cui, Shu Liu, Haomin Zhou
Journal of Dynamics and Differential Equations, Volume 36, pages 3885–3921, 2024.
PaperNeural parametric Fokker-Planck equations
Shu Liu, Wuchen Li, Hongyuan Zha, Haomin Zhou
SIAM Journal on Numerical Analysis, Vol. 60, Iss. 3, pp. 1385-1449, 2022
Paper | SlidesWhat is a stochastic Hamiltonian process on finite graph? An optimal transport answer
Jianbo Cui, Shu Liu, Haomin Zhou
Journal of Differential Equations, Vol. 305, Pages 428-457, 2021
Paper | SlidesA particle-evolving method for approximating the optimal transport plan
Shu Liu, Haodong Sun, Hongyuan Zha
Geometric Science of Information, 2021
Learning stochastic behaviour from aggregate data.
Shaojun Ma, Shu Liu, Hongyuan Zha, Haomin Zhou
Proceedings of the 38th International Conference on Machine Learning (ICML), 2021
PaperLearning high dimensional Wasserstein geodesics
Shu Liu∗, Shaojun Ma∗, Yongxin Chen, Hongyuan Zha, Haomin Zhou
arXiv:2102.02992. 2021
Paper