2025

2024

S. Liu, S. Osher, W.C. Li. A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations. Nov, 2024.

X.Z. Zuo, S. Osher, W.C. Li. Gradient-adjusted underdamped Langevin dynamics for sampling. Oct, 2024.

M. Zhou, S. Osher, W.C. Li. Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems. Sep, 2024.

F. Han, S. Osher, W.C. Li. Convergence of Noise-Free Sampling Algorithms with Regularized Wasserstein Proximals. Sep, 2024.

Y. Gao, W.C. Li, J.G. Liu. Fluctuations in Wasserstein dynamics on Graphs. Aug, 2024.

A. Vijaywargiya, G. Fu, S. Osher, W.C. Li. Efficient computation of mean field control based barycenters from reaction-diffusion systems. April, 2024.

T.W. Meng, S.T. Liu, W.C. Li, S. Osher. A primal-dual hybrid gradient method for solving optimal control problems and the corresponding Hamilton-Jacobi PDEs. March, 2024.

X.Z. Zuo, J.X. Zhao, S. Liu, S. Osher, W.C. Li. Numerical analysis on neural network projected schemes for approximating one dimensional Wasserstein gradient flows. Feb, 2024.

G. Fu, H. Ji, W. Pazner, W.C. Li. Mean field control of droplet dynamics with high order finite element computations. Feb, 2024.

B. Zhang, S. Liu, W.C. Li, M. Katsoulakis, S. Osher. Wasserstein proximal operators describe score-based generative models and resolve memorization. Feb, 2024.

Q. Feng, X.Z. Zuo, W.C. Li. Fisher information dissipation for time inhomogeneous stochastic differential equations. Feb, 2024.

S. Liu, X.Z. Zuo, S. Osher, W.C. Li. Numerical analysis of a first-order computational algorithm for reaction-diffusion equations via the primal-dual hybrid gradient method. Jan, 2024.

F. Han, S. Osher, W.C. Li. Tensor train based sampling algorithms for approximating regularized Wasserstein proximal operators. Jan, 2024.

M. Zhou, S. Osher, W.C. Li. A deep learning algorithm for computing mean field control problems via forward-backward score dynamics. Jan, 2024.

G. Fu, S. Osher, W. Pazner, W.C. Li. Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation. Accepted in Journal of Computational Physics, 2024.

S. Liu, S.T. Liu, S. Osher, W.C. Li. A first-order computational algorithm for reaction-diffusion type equations via primal-dual hybrid gradient method. Accepted in Journal of Computational Physics, 2024.

2023

W. Lee, Li Wang, W.C. Li. Deep JKO: time-implicit particle methods for general nonlinear gradient flows. Nov, 2023.

T. Meng, W. Hao, S. Líu, S. Osher, W.C. Li. Primal-dual hybrid gradient algorithms for computing time-implicit Hamilton-Jacobi equations. Oct, 2023.

W.C. Li, J.X. Zhao. Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Models. Sep, 2023.

Y. Li, H. Wang, W.C. Li. A time-fractional optimal transport and mean-field planning: Formulation and algorithm. Sep, 2023.

H.Y. Tan, S. Osher, W.C. Li. Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals. Aug, 2023.

W.C. Li. Langevin dynamics for the probability of Markov jumping processes. July, 2023.

W.C. Li, Tryphon Georgiou. Minimal Wasserstein Surfaces. June, 2023.

W.C. Li, L. Lu. Optimal Ricci curvature Markov chain Monte Carlo methods on finite states. Feb, 2023.

Y. Gao, W.C. Li, J.G. Liu. Master equations for finite state mean field games with nonlinear activations. Accepted in Discrete and Continuous Dynamical Systems Series B, Dec, 2023.

E. Bayraktar, Q. Feng, W.C. Li. Exponential Entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations. Accepted in Journal of Nonlinear Science, Oct, 2023.

W.C. Li, Diffusion hypercontractivity via generalized density manifold, accepted in Information Geometry, Oct, 2023.

W.C. Li, S. Liu, S. Osher. A kernel formula for regularized Wasserstein proximal operators, accepted in Research in the Mathematical Sciences, Sep 2023.

K.Elamvazhuthi, S. Liu, W.C. Li, S. Osher. Optimal Transport of Nonlinear Control-Affine Systems, accepted in Journal of Computational Dynamics, 2023.

Q. Feng, W.C. Li. Entropy dissipation via information Gamma calculus: non-reversible stochastic differential equations, accepted in poster session, Geometric Science of Information, 2023.

G. Fu, S. Osher, W.C. Li. High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems, accepted in Journal of Computational Physics, July, 2023.

G. Fu, S. Liu, S. Osher, W.C. Li. High order computation of optimal transport, mean field planning, and mean field games, accepted in Journal of Computational Physics, July, 2023.

X. Zuo, S. Osher, W.C. Li. Primal-dual damping algorithms for optimization, accepted in Annals of Mathematical Sciences and Applications, Jun, 2023.

Q. Feng, W.C. Li. Entropy dissipation for degenerate stochastic differential equations via sub-Riemannian density manifold (I), accepted in Entropy, May, 2023.

J. Yu, R. Lai, W.C. Li, S. Osher. A Fast Proximal Gradient Method and Convergence Analysis For Dynamic Mean Field Planning, accepted in Mathematics of Computation, 2023.

J. Yu, R.J. Lai, W.C. Li, S. Osher. Computational mean field games on manifolds, accepted in Journal of Computational Physics, 2023.

W.C. Li, S. Liu, S. Osher. Controlling conservation laws I: entropy-entropy flux, accepted in Journal of Computational Physics, Feb, 2023.

W.C. Li, J.X. Zhao. Wasserstein information matrix, accepted in Information Geometry. Jan, 2023.

2022

Y.F. Wang, P. Chen, M. Pilanci, W.C. Li. Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization. May, 2022.

W.C. Li, L.Y. Lu. Mean field information Hessian matrices on graphs. March, 2022.

W.C. Li, H. Park. Mean field Kuromoto models on graphs. March, 2022.

Q. Feng, W.C. Li. Hypoelliptic Entropy dissipation for stochastic differential equations (II). Renewed, Feb, 2022.

S. Liu, S. Osher, W.C. Li, C.W. Shu. A Primal-Dual approach for solving Conservation Laws with Implicit in Time Approximations, accepted in Journal of Computational Physics, Sep, 2022.

W.C. Li, F.J. Rubio. On a prior based on the Wasserstein information matrix, accepted in Statistics and Probability Letters, July, 2022.

W. Lee, S. Liu, W.C. Li, S. Osher. Mean field control problems for Vaccine distribution, accepted in Research in the Mathematical Sciences, 2022.

W.C. Li, W. Lee, S. Osher. Computational Mean-field information dynamics associated with Reaction diffusion equations, accepted in Journal of Computational Physics, 2022.

Y.F. Wang, P. Chen, W.C. Li. Projected Wasserstein gradient descent for high-dimensional Bayesian inference, accepted in SIAM/ASA Journal on Uncertainty Quantification, 2022.

W.C. Li, S. Liu, S. Osher. Controlling conservation laws II: compressible Navier-Stokes equations, accepted in Journal of Computational Physics, April, 2022.

L. Ding, W.C. Li, S. Osher, W. Yin. A mean field inverse problem, accepted in Journal of Scientific computing, March, 2022.

S. Liu, W.C. Li, H. Zha, H. Zhou. Neural parametric Fokker-Planck equation, accepted in SIAM numerical analysis, Jan, 2022.

2021

Y.F. Wang, W.C. Li. Accelerated Information Gradient flow, Journal of Scientific computing, Nov 2021. Website & Code

D. Jekel, W.C. Li, D. Shlyakhtenko. Tracial smooth functions of non-commuting variables and the free Wasserstein manifold, accepted in Dissertationes Mathematicae, Nov, 2021.

W.C. Li. Transport information Bregman divergences, acccepted in Information Geometry, Nov, 2021.

W.C. Li. Transport information geometry I: Riemannian calculus on probability simplex, accepted in Information Geometry, Nov, 2021.

A.T. Lin, W.C. Li, S. Osher, G. Montufar. Wasserstein Proximal of GANs, GSI, 2021.

S. Liu, M. Jacobs, W.C. Li, L. Nurbekyan, S. Osher. Computational methods for nonlocal mean field games with applications, SIAM journal on numerical analysis, 2021.

W. Lee, W.C. Li, B. Lin, A. Monod. Tropical Optimal Transport and Wasserstein Distances in Phylogenetic Tree Space, Information Geometry, 2021.

A.T. Lin, S. Fung, W.C. Li, L. Nurbekyan, S. Osher. APAC-Net: Alternating the Population and Agent Control via Two Neural Networks to Solve High-Dimensional Stochastic Mean Field Games, PNAS, 2020.

W.C. Li. Transport information Hessian distances. GSI, 2021.

W.C. Li. Hessian metric via transport information geometry, Journal of Mathematical Phyiscs, Jan, 2021.

2020

Y.F. Wang, W.C. Li. Information Newton flow: second-order optimization method in probability space, Jan, 2020.

W. Lee, S. Liu, H. Tembine, W.C. Li, S. Osher. Controlling propagation of epidemics via mean-field games, SIAM Journal on Applied Math, 2020.

W. Lee, R.J. Lai, W.C. Li, S. Osher. Generalized unnormalized optimal transport and its fast algorithms, Journal of Computational Physics, 2020.

S. Becker, W.C. Li. Quantum statistical learning via quantum Wasserstein natural gradient, Journal of Statistical Physics, 2020.

S.N. Chow, W.C. Li, C.C. Mou, H.M. Zhou. Dynamical Schrodinger bridge problems on graphs, Journal of Dynamics and Differential Equations, 2020.

F. Leger, W.C. Li. Hopf-Cole transformation via generalized Schrodinger bridge problem, Journal of Differential Equations, 2020.

J.L. Liu, W. Yin, W.C. Li, Y.T. Chow. Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances, SIAM Journal on Scientific Computing, 2020.

Y.F. Chen, W.C. Li. Optimal transport natural gradient in statistical manifolds with continuous sample space, Information geometry, 2020.

W.C. Li, J.F. Lu, L. Wang. Fisher information regularization schemes for Wasserstein gradient flows, Journal of Computational Physics, 2020.

L. Ruthottoa, S. Osher, W.C. Li, L. Nurbekyan, S. Fung. A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems, PNAS, March, 2020.

S.N. Chow, W.C. Li, J. Lu, H.M. Zhou. Equilibrium selection via optimal transport, SIAM Journal on Applied Math, Jan, 2020.

W.C. Li, G. Montufar. Ricci curvature for parameter statistics via optimal transport, Information Geometry, Jan, 2020.

2019

M. Arbel, A. Gretton, W. Li, G. Montufar. Kernelized Wasserstein Natural Gradient, ICLR, spotlight, 2020.

W.C. Li, L.X. Ying. Hessian transport gradient flows, Research in the Mathematical Sciences, 2019.

A. Garbuno-Inigo, F.Hoffmann, W.C. Li, A.M. Stuart. Interacting Langevin Diffusions: Gradient structure and ensemble Kalman sampler, SIAM Journal on applied dynamical system, 2019.

A.T. Lin, Y. Dukler, W.C. Li, G. Montufar. Wasserstein Diffusion Tikhonov Regularization, OTML Workshop NeurIPS, 2019.

W. Gangbo, W.C. Li, S. Osher, M. Puthawala. Unnormalized optimal transport, Journal of Computational Physics, 2019. . Appendix

S.N. Chow, W.C. Li, H. Zhou. Wasserstein Hamiltonian flows, Journal of differential equations, 2019.

W.C. Li, A.T. Lin, G. Montufar. Affine Natural Proximal Learning, Geometry science of information, 2019.

W.C. Li, S. Liu, H. Zha, H. Zhou. Parametric Fokker-Planck equation, Geometry science of information, 2019.

F. Leger, W.C. Li. Hopf--Cole Transformation and Schrodinger Problems, Geometry science of information, 2019.

Y. Dukler, W.C. Li, A.T. Lin, G. Montufar. Wasserstein of Wasserstein Loss for Learning Generative Models, ICML, Long Beach, April, 2019.

Y.T. Chow, W.C. Li, S. Osher, W. Yin. Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula, Journal of Scientific Computing, 2019.

M. Jacobs, F. Leger, W.C. Li, S. Osher. Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size, SIAM Journal on Numerical Analysis, 2019.

S.N. Chow, W.C. Li, H.M. Zhou. A discrete Schrodinger equation via optimal transport on graphs, Journal of Functional analysis, 2019.

2018

W.C. Li, S. Osher. Constrained dynamical optimal transport and its Lagrangian formulation, note, 2018.

W.C. Li, G. Montufar. Natural gradient via optimal transport, Information Geometry, Dec, 2018.

S.N. Chow, W.C. Li, J. Lu, H.M. Zhou. Population games and discrete optimal transport, Journal of Nonlinear Science, 2018.

W. Gangbo, W.C. Li, C.C. Mou. Geodesic of minimal length in the set of probability measures on graphs, ESAIM: Control, Optimisation and Calculus of Variations (ESAIM:COCV), 2018.

S.N. Chow, L. Dieci, W.C. Li, H.M. Zhou. Entropy dissipation semi schemes for Fokker-Planck equations, Journal of Dynamics and Differential Equations, 2018.

E. Ryu, Y.X. Chen, W.C. Li, S. Osher. Vector and Matrix Optimal Mass Transport: Theory, Algorithm, and Applications, SIAM Journal on Scientific Computing, 2018.

S.N. Chow, W.C. Li, H.M. Zhou. Entropy dissipation of Fokker-Planck equations on finite graphs, Discrete & Continuous Dynamical Systems-Series A, 2018.

2017

W.C. Li, P. Yin, S. Osher. Computations of optimal transport distance with Fisher information regularization, Journal of Scientific Computing, 2017.

E. Ryu, W.C. Li, P. Yin, S. Osher. Unbalanced and Partial L1 Monge--Kantorovich Problem: A Scalable Parallel First-Order Method, Journal of Scientific Computing, 2017.

W.C. Li, M. Egerstedt, S.N. Chow, J. Lu, H.M. Zhou. Method of evolving junctions: A new approach for the optimal path-planning in a dynamic environment, International Journal of Robotics Research, 2017.

W.C. Li, E. Ryu, S. Osher, W. Yin, W. Gangbo. A Parallel Method for Earth's Movers Distance, Journal of Scientific Computing, 2017.

S.N. Chow, W.C. Li, J. Lu, H.M. Zhou. Method of evolving junctions: A new approach to optimal control with constraints, Automatica, 2017.

2016

W.C. Li. A study of stochastic differential equations and Fokker-Planck equations with applications, Ph.D. thesis, 2016.

L. Dieci, W.C. Li, H.M. Zhou. A new model for realistic random perturbations of stochastic oscillators, Journal of differential equations, 2016.

S.N. Chow, W.C. Li, H.M. Zhou. A Newton-like algorithm for the shortest path based on the method of evolving junctions, Communications in Mathematical Sciences, 2016.