Updated 02/01/2020.

Theortical Data Science

Transport information optimziation and MCMC

  • Y.F. Wang, W.C. Li. Information Newton flow: second-order optimization method in probability space, submitted, Jan, 2020.
  • Y.F. Wang, W.C. Li. Accelerated Information Gradient flow, submitted, Sep, 2019. [PDF]

Transport information geometry and Statistics

  • W.C. Li, J.X. Zhao. Wasserstein information matrix, submitted, Oct, 2019. [PDF]

Computational Machine learning

Computational Mean field games

  • 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, submitted, Dec, 2019. [PDF]

Kernalized methods

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

Deep learning methods

  • A.T. Lin, Y. Dukler, W.C. Li, G. Montufar. Wasserstein Diffusion Tikhonov Regularization, OTML workshop in NeurIPS, Oct, 2019. [PDF]
  • Y. Dukler, W.C. Li, A.T. Lin, G. Montufar. Wasserstein of Wasserstein Loss for Learning Generative Models, ICML, Long beach, April, 2019. [PDF]
  • W.C. Li, A.T. Lin, G. Montufar. Affine Natural Proximal Learning, GSI, 2019.[PDF]
  • A.T. Lin, W.C. Li, S. Osher, G. Montufar. Wasserstein Proximal of GANs, submitted, Sep, 2018. [PDF]

Deep Fluid dynamics

  • W.C. Li, S. Liu, H. Zha, H. Zhou. Parametric Fokker-Planck equation, GSI, 2019. [PDF]
  • W.C. Li, S. Osher. Constrained dynamical optimal transport and its Lagrangian formulation, note, 2018. [PDF]

Statistical learning

  • W.C. Li, G. Montufar. Natural gradient via optimal transport, Information Geometry, Dec, 2018. [PDF]
  • W.C. Li, G. Montufar. Ricci curvature for parameter statistics via optimal transport, submitted, 2018.[PDF]
  • Y.F. Chen, W.C. Li. Wasserstein natural gradient in statistical manifolds with continuous sample space, submitted, 2018. [PDF]

Density manifold

  • W.C. Li. Geometry of probability simplex via optimal transport, submitted, 2018. [PDF]
  • W.C. Li. Diffusion hypercontractivity via generalized density manifold, submitted, Oct, 29, 2019.[PDF]
  • Q. Feng, W.C. Li. Generalized Gamma z calculus via sub-Riemannian density manifold, submitting, 2019. [PDF]

Optimal transport and Mean field Games

Unnormalized Optimal Transport/Mean field games

  • W. Gangbo, W.C. Li, S. Osher, M. Puthawala. Unnormalized optimal transport, Journal of Computational Physics, Sep, 2019. [PDF][APPENDIX]
  • W.J. Lee, R.J. Lai, W.C. Li, S. Osher. Fast algorithms for generalized unnormalized optimal transport, submitted, Feb, 2019. [PDF]

Numerical Mean field Games

  • 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. [PDF]

Eovlutionary Games

  • S.N. Chow, W.C. Li, J. Lu, H.M. Zhou. Population games and discrete optimal transport, Journal of Nonlinear Science, Oct, 2018. [PDF]
  • S.N. Chow, W.C. Li, J. Lu, H.M. Zhou. Equilibrium selection via optimal transport, SIAM jouranl on Applied Math, Sep, 2019. [PDF]
  • W. Gangbo, W.C. Li, C.C. Mou. Geodesic of minimal length in the set of probability measures on graphs, ESAIM:COCV, Sep, 2018. [PDF]

Computational Fluid dynamics

  • W.C. Li, P. Yin, S. Osher. Computations of optimal transport distance with Fisher information regularization, Journal of Scientific Computing, June, 2017. [PDF]
  • 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.[PDF]
  • W.C. Li, J.F. Lu, L. Wang. Fisher information regularization schemes for Wasserstein gradient flows, submitted, July, 2019. [PDF]

Scientific Computing

  • 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. [PDF][CODE]
  • 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. [PDF]
  • 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. [PDF][CODE]
  • 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. [PDF]
  • J.L. Liu, W. Yin, W.C. Li, Y.T. Chow. Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances, submitted, 2018. [PDF][CODE]

Stochastics Differential equations

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. [PDF]

Hessian transport

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

Algebraic Geometry

  • W. Lee, W. Li, B. Lin, A. Monod. Tropical Optimal Transport and Wasserstein Distances in Phylogenetic Tree Space, submitted, 2019. [PDF]

Dynamical System

Schrodinger equations

  • S.N. Chow, W.C. Li, H. Zhou. Wasserstein Hamiltonian flows, Journal of differential equations, August, 2019. [PDF]
  • S.N. Chow, W.C. Li, H.M. Zhou. A discrete Schrodinger equation via optimal transport on graphs, Journal of Functional analysis, Feb, 2019. [PDF]
  • 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. [PDF]

Schrodinger bridge problems

  • F. Leger, W.C. Li. Hopf--Cole Transformation and Schrodinger Problems, GSI, 2019. [PDF]
  • S.N.Chow, W.C. Li, C.C. Mou, H.M. Zhou. A discrete Schrodinger bridge problem via optimal transport on graphs, submitted, 2018. [PDF]
  • F. Leger, W.C. Li. Hopf-Cole transformation via generalized Schrodinger bridge problem, submitted, 2019. [PDF]

Optimal contorl and Robotics path planning

  • 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, May, 2017. [PDF]
  • S.N. Chow, W.C. Li, J. Lu, H.M. Zhou. Method of evolving junctions: A new approach to optimal control with constraints, Automatica, April, 2017. [PDF]
  • 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, Jan, 2016. [PDF]
  • L. Dieci, W.C.Li, H.M. Zhou. A new model for realistic random perturbations of stochastic oscillators, Journal of differential equations, May, 2016. [PDF]
  • Wuchen Li. A study of stochastic differential equations and Fokker-Planck equations with applications, Ph.D. thesis, 2016. [PDF]