Probability manifold via optimal transport

Geometry

  • W.C. Li. "Geometry of probability simplex via optimal transport", submitted, 2018. [pdf]

Gradient flow

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

Hamiltonian flow

  • S.N. Chow, W.C. Li, H.M. Zhou, "A discrete Schrodinger equation via optimal transport on graphs", submitted, 2017. [pdf]
  • W. Gangbo, W.C. Li, M. Chen, "Geodesic of minimal length in the set of probability measures on graphs", submitted, 2017. [pdf]
  • W.C. Li, P. Yin, S. Osher, "Computations of optimal transport distance with Fisher information regularization", Journal of Scientific Computing, 2017.[pdf]

Wasserstein statistical manifold and Machine learning

  • W.C. Li, G. Montufar. "Natural gradient via optimal transport I", submitted, 2018. [pdf]
  • Y.F. Chen, W.C. Li. "Natural gradient in Wasserstein statistical manifold", submitted, 2018. [pdf]

Mean field games

  • S.N. Chow, W.C. Li, J. Lu, H.M. Zhou, "Equilibrium selection via optimal transport", submitted, 2017. [pdf]
  • S.N. Chow, W.C. Li, J. Lu, H.M. Zhou, "Population games and Discrete optimal transport", submitted, 2017. [pdf]
  • Y.T. Chow, W.C. Li, W. Yin, S. Osher, "Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula", submitted, 2018. [pdf]

L1 optimal transport with applications

  • W.C. Li, E. Ryu, S. Osher, W. Yin, W. Gangbo, " A Parallel Method for Earth's Movers Distance", Journal of Scientific Computing, 2017. [pdf]
  • E.Ryu, W.C. Li, P. Yin, S. Osher, "A Fast Algorithm for Unbalanced L1 Monge-Kantorovich Problem", Journal of Scientific Computing, 2017. [pdf]
  • Y.P. Li, W.C. Li, G. Cao, "Image Segmentation via L1 Monge-Kantorovich Problem", submitted, 2017. [pdf]
  • E. Ryu, Y.X. Chen, W.C. Li, S. Osher, "Vector and Matrix Optimal Mass Transport: Theory, Algorithm, and Applications", submitted, 2017. [pdf]
  • M. Jacobs, F. Leger, W.C. Li, S. Osher, "Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size", submitted, 2018. [pdf]

Optimal control with constraints

  • 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. [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, 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, 2016. [pdf]

Stochastic differential equations

  • L. Dieci, W.C.Li, H.M. Zhou, "A new model for realistic random perturbations of stochastic oscillators", Journal of differential equations, 2016. [pdf]
  • Wuchen Li, "A study of stochastic differential equations and Fokker-Planck equations with applications", Ph.D. thesis, 2016. [pdf]