Transport information calculus

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

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

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

Transport information modeling and computation of complex systems

Stochastic control

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

Kernel methods

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

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

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

PDHG for computing conservation laws and reaction-diffusions

S. Liu, X. 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.

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.

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. May, 2023.

S. Liu, S. Osher, W.C. Li, C.W. Shu. A Primal-Dual approach for solving Conservation Laws with Implicit in Time Approximations. July 15, 2022.

Neural network models

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.

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

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 journal on numerical analysis, 2022. . GSI, 2019.

M. Arbel, A. Gretton, W.C. Li, G. Montufar. Kernelized Wasserstein Natural Gradient. ICLR 2020 (International Conference on Learning Representations), spotlight, Dec, 2019.

PDE models

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

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. Accepted in Research in the Mathematical Sciences, July 7, 2022.

F. Leger, W.C. Li. Hopf-Cole transformation via generalized Schrodinger bridge problem. Journal of Differential Equations, 2020. . GSI, 2019.

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. Accepted in Research in Mathematical Science, April 24, 2021.

Finite Elements

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

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

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, 2024.

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, 2023.

Manifolds and Triangular meshes

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

Graph models

W.C. Li, H. Park. Mean field Kuromoto models on graphs. March 3, 2022.

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

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

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.

Transport information Optimization and Markov Chain Monte Carlo methods

Optimizations for Inverse problems

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.

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

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. Accepted in SIAM/ASA Journal on Uncertainty Quantification, June 2022.

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

Time discretizations

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

Transport information convexity analysis on PDEs and Stochastic dynamics

Hessian matrix of flux-gradient flows

TBA

Hessian matrix of linear Fokker-Planck equations and stochastic dynamics

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

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

Q. Feng, W.C. Li. Entropy dissipation for degenerate stochastic differential equations via sub-Riemannian density manifold (I). Renewed and combined with "sub-Riemannian Ricci curvature", Feb, 2022.

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

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

Hessian matrix of nonlinear Fokker-Planck equations and mean field dynamics

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.

Transport information analysis on Neural networks and Graphs

Hessian matrix of mean field dynamics on neural networks

TBA

Hessian matrix of mean field dynamics on graphs

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

Transport information statistics

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

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

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

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

Quantum transport information

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 scientific computing

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 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.

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. Mathematics of Computation , 2023.

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.

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. 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. Dynamical optimal transport of nonlinear control-affine systems . Journal of Computational Dynamics, 2023.

Tropical Geometry

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

Transport information inverse problems

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

Thesis

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