Wuchen Li

Assistant professor in Mathematics at University of South Carolina.

Optimal transport and Mean field games seminar, Fall 2021.

News

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.

Draft "Mean field control problems for Vaccine distribution" is online. We design mean field control problems for optimal spatial distribution of vaccine. April 24, 2021.

Draft "A Fast Proximal Gradient Method and Convergence Analysis For Dynamic Mean Field Planning" is online. We design proximal gradient algorithms for a class of mean field planning problems and conduct related numerical analysis. Feb 26, 2021.

Draft "Projected Wasserstein gradient descent for high-dimensional Bayesian inference" is online. We apply first order transport optimization methods to design algorithms in inverse problems and Bayesian inferences. Feb 16, 2021.

Draft "Transport information Hessian distances" is online. We derive closed-form solutions for Hessian distances of information entropies in Wasserstein space. They are distances in term of Jacobi operators of pushforward mapping functions, namely "optimal Jacobi transport distances". We will apply the proposed distances in AI inference problems and MCMC algorithms. Feb 8, 2021.

Draft "Hypoelliptic Entropy dissipation for stochastic differential equations" is online. We derive a structure condition and an algebraic tensor to estimate the convergence rates of variable coefficients degenerate Langevin dynamics. Our method is based on a weighted Fisher information induced Gamma derivative method. We will apply the result to design degenerate MCMC algorithms with theoretical convergence guarantees. Feb 1, 2021.

Draft "Tracial smooth functions of non-commuting variables and the free Wasserstein manifold" is online. We study the optimal transport metric in free probabilties. It can be viewed as a natural first step to develop free transport information geometry. Jan 18, 2021.

Draft "Transport information Bregman divergences" is online. We study Bregman divergences in Wasserstein-2 space. In particular, we derive the transport Kullback-Leibler (KL) divergence, which is a Bregman divergence of negative Boltzmann-Shannon entropy in Wasserstein-2 space. Here the transport KL divergence is an Itakura–Saito type divergence in transport coordinates. Jan 4, 2021.

Previous results

Research interests

Transport information science in Data science, Geometry, Complex Dynamical systems, Graphs, Computation, Control and Games.

Recent Publications

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.

Our paper "Transport information geometry: Riemannian calculus on probability simplex", is accepted in Information Geometry, 2021.

Our paper "Transport information Hessian distances" is accepted in Geometry Science of Information, 2021.

Our paper "Wasserstein proximal of GANs" is accepted in Geometry Science of Information, 2021.

Our paper "Computational methods for nonlocal mean field games with applications" is accepted in SIAM journal on Numerical Analysis, 2021.

Our paper "ApacNet: An Alternating Population-Agent Control Neural Network for High-Dimensional Stochastic Mean Field Games" is accepted in Proceedings of the National Academy of Sciences of the United States of America (PNAS), 2021.

Our paper "Tropical optimal transport and Wasserstein distance in Phylogenetic Tree Space" is accepted in Information Geometry, 2021.

Our paper "Hessian metric via transport information geometry" is accepted in Journal of Mathematical Physics, Jan, 2021.

Our paper "Controlling Propagation of epidemics via mean-field control" is accepted in SIAM Journal on Applied Math, Dec, 2020.

Our paper "Generalized Unnormalized Optimal Transport and its fast algorithms" is accepted in Journal of Computational Physics, Nov, 2020.

Our paper "Quantum statistical learning via quantum Wasserstein natural gradient " is accepted in Journal of Statistical Physics. Nov, 2020.

Our paper "Dynamical Schrodinger bridge problems on graphs" is accpeted in Journal of Dynamics and Differential Equations, Nov, 2020.

Our paper "Hopf-Cole transform via generalized Schrodinger bridge problem" is accepted in Journal of Differential Equations, Oct, 2020.

Our paper ''Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances'' is accpeted in SIAM Journal on Scientific Computing, Sep 2020.