Wuchen Li

Assistant professor in Mathematics at University of South Carolina.

Google Scholar

Optimal transport and Mean field games seminar, Spring 2022.

Recent News

Draft "Exponential Entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations" is online. We study "Hessian matrices" for a kinectic Fokker-Planck equation with mean field interaction energy. Exponential convergence result in L1 distance is proved. Two examples of convergence rates are provided. April 27, 2022.

Draft "Mean field information Hessian matrices on graphs" is online. We study Hessian matrices of general energies in a graphic optimal transport metric space. A new mean field function namely transport information mean is introduced. A discrete Costa's entropy power inequality on a two point graph is derived. March 14, 2022.

Draft "Mean field Kuromoto models on graphs" is online. We study a mean field synnorization model on discrete domain using optimal transport on graphical models. A generalized Hopf-Cole transformation is studied. Analytical examples of synnorization models on two point graphs are discussed. March 3, 2022.

Draft "Entropy dissipation for degenerate stochastic differential equations via sub-Riemannian density manifold (I) " is renewed. We provide a new example of the exponential entropy convergence analysis for one dimensional degenerate SDEs, Feb 28, 2022.

Draft "Controlling conservation laws II: compressible Navier-Stokes equations" is online. We propose and compute solutions to a class of optimal control problems for barotropic compressible Navier-Stokes equations. Feb 23, 2022.

Draft "On a prior based on the Wasserstein information matrix" is online. We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix. Several examples of Wasserstein priors, in particular skew Gaussian distributions, are presented. This is a natural second step for transport information statistics, Feb 8, 2022.

Draft "Hypoelliptic entropy dissipation for stochastic differential equations (II)" is renewed. We provide one more example of the Lyapunov convergence analysis for 3 oscillator chain, Feb 1, 2022.

Draft "Controlling conservation laws I: entropy-entropy flux" is online. We propose to study a class of mean field control problems for conservation laws with entropy-entropy flux pairs. A variational structure, namely flux-gradient flows and their dual equations in entropy-entropy flux pair metric spaces, are introduced. The control of flux-gradient flows are useful in modeling complex dynamics and designing implicit time schemes for conservation laws, Nov 10, 2021.

Draft "Computational Mean-field information dynamics associated with Reaction diffusion equations" is online. We compute a general mean field control problems arised from nonlinear reaction diffusion equations. July 26, 2021.

Previous results

Research interests

Transport information geometry in PDEs, Data, Graphs and Neural networks, Complex Dynamical systems, Computation, Statistics, Control and Games.

Recent Publications

Our paper "Controlling conservation laws II: compressible Navier-Stokes equations" is accepted in Journal of Computational Physics, 2022.

Our paper "A mean field game inverse problem" is accepted in Journal of Scientific Computing, 2022.

Our paper "Neural parametric Fokker-Planck equation" is accepted in SIAM journal on numerical analysis, 2022.

Our paper "Accelerated information gradient flow" is accepted in Journal of Scientific Computing, 2021.

Our paper "Transport information Bregman divergences" is accepted in Information Geometry, 2021.

Our paper "Tracial smooth functions of non-commuting variables and the free Wasserstein manifold" is accepted in Dissertationes Mathematicae, 2021.