Assistant professor in Mathematics at University of South Carolina.
Optimal transport and Mean field games seminar, Spring 2022.
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 "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.
Transport information geometry in PDEs, Data, Graphs and Neural networks, Complex Dynamical systems, Computation, Statistics, Control and Games.
© 2020 Wuchen Li