• Short biography

    • I am moving to University of South Carolina as an assistant professor.
    • UCLA, CAM assistant professor in Mathematics, 2016-2020.
    • Georgia Tech, Ph.D. in Mathematics, 2016.
    • Georgia Tech, M.S. in Statistics, 2015.
    • Shandong University, B.S.in Mathematics, 2009.

    Research areas

      Google Scholar.
    • Transport information geometry with applications in Data science;
    • Mean field games, optimal transport, Schrodinger equation and Schrodinger Bridge problem;
    • Transport information scientific computing and modeling.

    Website Links

    News

    • Draft "Accelerate information gradient flow" is renewed. We further introduce several interesting accelerated gradient flows, based on the Kalman-Wasserstein metric and the Stein metric. Several ''accelerated'' interacting particle dynamics are designed for Bayesian sampling problems. Numerical examples of Bayesian regression problems demonstrate the effectiveness of their acceleration effects. June 2, 2020. [PDF]
    • Draft "Controlling propagation of epidemics via mean-field games" is online. We introduce a mean-field SIR model for controlling the propagation of epidemics, such as COVID 19. We design the spatial SIR models with the population's velocity field as control variables. Numerical experiments demonstrate that the proposed model illustrates how to separate infected patients in a spatial domain effectively. June 1, 2020. [PDF]
    • We apply primal-dual algorithms to solve Mean field games with nonlocal interaction energies. Several applications of kernels, including robotic path planning problems, are demonstrated. [PDF].
    • Paper "Optimal transport natural gradient in statistical manifold with continuous sample space" has been accepted in Information geometry. April 14, 2020.
    • We formulate generalized Ricci curvature tensors and Bochner's formula in a sub-Riemannian manifold. Several analytical examples, including the Hessenberg group, the Displacement group, and Martinet sub-Riemannian structure, have been given. April 6, 2020. [PDF]
    • Our paper "Fisher information regularization schemes for Wasserstein gradient flows" has been accepted in Journal of Computational Physics. March 31, 2020.
    • Draft "Optimal Transport of Nonlinear Control-Affine Systems" is online. We study the reachability and numerically compute optimal transport with sub--Riemannian or control affine structures. March 30, 2020. [PDF]
    • Draft "Hessian metric via transport information geometry" is online. We extend and contain the classical optimal transport metric to the Hessian metrics. We observe that there are several connections with math physics equations. In particular, the transport Hessian Hamiltonian flow of negative Boltzmann--Shannon entropy satisfies the Shallow Water's equation; The transport Hessian metric is a particular mean field Stein metric. The transport Hessian metrics would be useful in designing Bayesian sampling algorithms and AI inferences. March 23, 2020. [PDF]
    • Our paper "A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems" has been accepted in PNAS. March 2020.
    • Draft "Neural Fokker--Planck equation" is online. We propose Fokker-Planck equations within machine learning generative models. This approach allows us to approximate high dimensional Fokker-Planck equations. A neural kernelized mean-field stochastic differential equation is proposed. Numerical examples and analysis are provided. February 26, 2020. [PDF]
    • Draft "Neural primal dual method" is online. We combine the generative adversary networks and primal-dual algorithms to solve general mean-field games. Here the primal (density) and dual (potential) variables are approximated by generators and discriminators, respectively. This method allows us to approximate the solution including 50 dimensions. Feb 24, 2020. [PDF]
    • Draft "Information Newton flow: second-order optimization method in probability space" is online. We propose information Newton's flows for sampling optimization problems arisen in inverse problems and Bayesian statistics. Newton's Langevin dynamics, a.k.a Wasserstein Newton's flows of KL divergence, are derived. These can be viewed as a second-order algorithm for Bayesian sampling problems. Jan 13, 2020. [PDF]
    • Paper "Ricci curvature for parametric statistics via optimal transport" has been accepted in Information Geometry. January 12, 2020.
    • Paper "Kernelized Wasserstein Natural Gradient" is accepted in ICLR 2020, Spotlight. Dec 20, 2019.
    • Old news up to 2019.

    Highlights

    Mean Field Games with Applications 2. [Under construction]
    Wasserstein Information Matrix [Talk ] [Paper1]
    Mean field SIR game [Talk ] [Paper]
    Neural Fokker-Planck equation [Talk ][Paper]
    Ricci curvature for degenerate diffusion process [Talk ]
    Transport information geometry: current and future [Talk ]
    Transport information Newton's flow [Talk ] [Paper]
    Mean Field Games with Applications 1. [Overview Talk ] [Generative network Talk]
    Accelerated Information Gradient flow. [Talk ] [pdf ]
    Unnormalized Optimal Transport. [Talk ] [pdf1][pdf2]
    Transport information geometric learning. [Talk ] [pdf1 ][pdf2] [pdf3] [pdf4][ pdf5 ][ pdf6 ]
    Evolutionary games via optimal transport. [Talk ] [pdf1 ][pdf2 ]
    Computational Mean field games. [Talk ] [pdf ]
    Hamiltonian flows via optimal transport. [Talk1] [Talk2] [pdf1 ][pdf 2][ pdf3] [pdf4]
    Gradient flows on graphs via optimal transport. [Talk ] [pdf1 ] [pdf2 ]
    L1 optimal transport with applications. [Talk ] [pdf1] [pdf2] [pdf3] [pdf4][pdf5]

    Contact

    • Office: MS 7620F, UCLA.
    • Email: wcli at math.ucla.edu