Transport information geometry

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

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

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

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



Transport information complex dynamical systems

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.

F. Leger, W.C. Li. Hopf-Cole Transformation and Schrodinger Problems, GSI, 2019.

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



Quantum transport information geometry

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.

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



Transport information analysis of linear/nonlinear PDEs and stochastic dynamics

W.C. Li. Diffusion hypercontractivity via generalized density manifold, Oct 29, 2019.

Q. Feng, W.C. Li. Sub-Riemannian Ricci curvature via generalized Gamma z calculus, April 6, 2020.

Q. Feng, W.C. Li. Generalized Gamma z calculus via sub-Riemannian density manifold, June 12, 2020.

Q. Feng, W.C. Li. Entropy dissipation via information Gamma calculus: non-reversible stochastic differential equations, Nov 16, 2020.

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



Transport information statistics, optimization and MCMC

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

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

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

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



Transport information inverse problems

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



Computational transport information geometry

Neural transport fluid dynamics

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

Neural Mean field games

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, Proceedings of the National Academy of Sciences (PNAS), 2021.

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, Proceedings of the National Academy of Sciences (PNAS), March, 2020.

Transport kernelized methods

M. Arbel, A. Gretton, W.C. Li, G. Montufar. Kernelized Wasserstein Natural Gradient, ICLR2020 (International Conference on Learning Representations), spotlight, Dec, 2019.

Transport proximal

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

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

W.C. Li, A.T. Lin, G. Montufar. Affine Natural Proximal Learning, GSI, 2019.

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

Transport natural gradient

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

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

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

S. Liu, W.C. Li, H.Y. Zha, H.M. Zhou. Neural Fokker-Planck equation, SIAM numerical analysis, 2022.

W.C. Li, S. Liu, H.Y. Zha, H.M. Zhou. Parametric Fokker-Planck equation, GSI, 2019.



Mean field information scientific computing

Mean field control and reaction diffusions

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

W.J. Lee, R.J. Lai, W.C. Li, S. Osher. Generalized Unnormalized Optimal Transport and its fast algorithms, Journal of Computational Physics, Nov, 2020.

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

Numerical Mean field Games

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

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

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.

Evolutionary Games

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

S.N. Chow, W.C. Li, J. Lu, H.M. Zhou. Equilibrium selection via optimal transport, SIAM Jouranl on Applied Math, Sep, 2019.

W. Gangbo, W.C. Li, C.C. Mou. Geodesic of minimal length in the set of probability measures on graphs, ESAIM:COCV, Sep, 2018.

Computational optimal transport

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

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, April, 2018.

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

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

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, Oct, 2018.

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, March, 2019.

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.

K.Elamvazhuthi, S. Liu, W.C. Li, S. Osher. Optimal Transport of Nonlinear Control-Affine Systems, 2020.

Kalman Filtering

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 sysetm, 2019.

Hessian transport

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

Tropical Geometry

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

Dynamics on graphs

S.N. Chow, W.C. Li, C.C. Mou, H.M. Zhou. A discrete Schrodinger bridge problem via optimal transport on graphs, accpeted in Journal of Dynamics and Differential Equations, 2020.

S.N. Chow, W.C. Li, H.M. Zhou. Wasserstein Hamiltonian flows, Journal of Differential Equations, August, 2019.

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

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



Others

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

© 2020 Wuchen Li