2022

S. Liu, W.C. Li, H. Zha, H. Zhou. Neural parametric Fokker-Planck equation, accepted in SIAM numerical analysis, Jan 24, 2022.

2021

W.C. Li, S. Liu, S. Osher. Controlling conservation laws I: entropy-entropy flux. Nov 10, 2021.

W.C. Li, W. Lee, S. Osher. Computational Mean-field information dynamics associated with Reaction diffusion equations. July 26, 2021.

W. Lee, S. Liu, W.C. Li, S. Osher. Mean field control problems for Vaccine distribution. April 24, 2021.

J. Yu, R. Lai, W.C. Li, S. Osher. A Fast Proximal Gradient Method and Convergence Analysis For Dynamic Mean Field Planning. Feb 26, 2021.

Y.F. Wang, P. Chen, W.C. Li. Projected Wasserstein gradient descent for high-dimensional Bayesian inference. Feb 16, 2021.

Q. Feng, W.C. Li. Hypoelliptic Entropy dissipation for stochastic differential equations. Feb, 2021.

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

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

Q. Feng, W.C. Li. Entropy dissipation via information Gamma calculus: non-reversible stochastic differential equations, Nov, 2020.

L. Ding, W.C. Li, S. Osher, W. Yin. A mean field inverse problem, July, 2020.

Qi Feng, W.C. Li. Sub-Riemannian Ricci curvature via generalized Gamma z calculus, April 3, 2020.

K.Elamvazhuthi, S. Liu, W.C. Li, S. Osher. Optimal Transport of Nonlinear Control-Affine Systems, March 30, 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

W.C. Li, J.X. Zhao. Wasserstein information matrix, Nov, 2019. .

Q. Feng, W.C. Li. Generalized Gamma z calculus via sub-Riemannian density manifold (104 pages), Oct, 2019.

W.C. Li, Diffusion hypercontractivity via generalized density manifold, Oct 29, 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.



© 2020 Wuchen Li