Wuchen Li. Department of Mathematics UCLA
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1 Wuchen Li Department of Mathematics UCLA Current Positions Education Computational and Applied Mathematics Assistant Professorship, UCLA, July, 2016 to present. Georgia Institute of Technology, Atlanta, USA Aug, 2011 to May, 2016 Ph.D. in Mathematics Georgia Institute of Technology, Atlanta, USA Aug, 2011 to May, 2016 Master in Statistics Chinese Academy of Science, Beijing, China Sep, 2009 to Jun, 2011 Computational Mathematics Shandong University, Jinan, China Sep, 2005 to Jun, 2009 Bachelor in Mathematics Research interest (i) Wasserstein information theory and Machine learning; (ii) Mean field games; (iii) Numerical optimal transport. Teaching experience Awards Leading Instructor Math 151B Applied numerical method (Spring 2017, Winter 2017, Spring 2018) Math 151A Applied numerical method (Winter 2018) Math 2605 Calculus 3 for Computer Science (Spring 2015, 95 students) Math 3215 Probability (Summer 2015, 30 students) Teaching Assistant Math 2403 Differential Equations (Spring 2013) Math 2401 Calculus III (Spring, Summer, Fall 2012, Summer, Fall 2013) Math 2605 Calculus 3 for Computer Science (Fall 2014) 1. Georgia Tech Best Thesis award, Bob Price Travel Fellowship, Georgia Tech, First scholarship, Shandong University, 2006.
2 Selected Work Publications 1. Wuchen Li. Geometry of probability simplex via optimal transport, 2. Shui-Nee Chow, Wuchen Li, Haomin Zhou. A discrete Schrödinger equation via optimal transport on graphs, Journal of Functional Analysis, Wuchen Li, Guido Montufar. Natural gradient via optimal transport, Information Geometry, 4. Flavien Leger, Wuchen Li. Hopf-Cole transform via generalized Schrödinger bridge problem, 5. Wilfrid Gangbo, Wuchen Li, Stanley Osher, Michael Puthawala. Unnormalized optimal transport, Matt Jacobs, Flavien Leger, Wuchen Li, Stanley Osher. Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size, accepted in SIAM journal on Numerical Analysis, Shui-Nee Chow, Wuchen Li, Haomin Zhou. A discrete Schrödinger equation via optimal transport on graphs, Journal of Functional Analysis, Yupeng Li, Wuchen Li, Guo Cao. Image Segmentation via L1 Monge-Kantorovich Problem, accepted in Inverse problem and Imaging, Wuchen Li, Guido Montufar. Natural gradient via optimal transport, Information Geometry, 5. Shui-Nee Chow, Wuchen Li, Jun Lu, Haomin Zhou. Population games and Discrete optimal transport, Journal of Nonlinear Science, 6. Wilfrid Gangbo, Wuchen Li, Chenchen Mou. Geodesic of minimal length in the set of probability measures on graphs, ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV), 7. Ernest Ryu, Yongxin Chen, Wuchen Li, Stanley Osher. Vector and Matrix Optimal Mass Transport: Theory, Algorithm, and Applications, SIAM Journal on Scientific Computing, 8. Shui-Nee Chow, Wuchen Li, Haomin Zhou. Entropy dissipation on finite graphs, Discrete and Continuous Dynamical Systems-Series A, 9. Shui-Nee Chow, Luca Dieci, Wuchen Li, Haomin Zhou. Entropy dissipation semi-discretization schemes for Fokker-Planck equations, Journal of Dynamics and Differential Equations, 10. Ernest Ryu, Wuchen Li, Penghang Yin, Stanley Osher. Unbalanced and Partial L1 Monge- Kontorovich Problem: A Scalable Parallel First-Order Method, Journal of Scientific Computing, Wuchen Li, Penghang Yin, Stanley Osher. Computation of optimal transport distance with Fisher information regularization, Journal of Scientific computing, Wuchen Li, Ernest Ryu, Stanley Osher, Wotao Yin, Wilfrid Gangbo. A parallel method for Earth Mover s distance, Journal of Scientific computing, Wuchen Li, Shui-Nee Chow, Magnus Egerstedt, Jun Lu, and Haomin Zhou. Method of evolving junctions: A new approach for the optimal path-planning in a dynamic environment, The International Journal of Robotics Research, Shui-Nee Chow, Wuchen Li, Jun Lu, Haomin Zhou. Method of evolving junctions: A new approach to optimal control with constraints, Automatica, Shui-Nee Chow, Wuchen Li, Haomin Zhou. A Newton-like algorithm for the shortest path based on the method of evolving junctions, Communications in mathematical sciences, Luca Dieci, Wuchen Li, Haomin Zhou. A new model for realistic random perturbations of stochastic oscillators, Journal of Differential equations, 2016.
3 Preprint Presentations 1. Shui-Nee Chow, Wuchen Li, Chenchen Mou, Haomin Zhou. A discrete Schrödinger bridge problem via optimal transport on graphs. 2. Jialin Liu, Wotao Yin, Wuchen Li, Yat Tin Chow. Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances. 3. Alex Lin, Wuchen Li, Stanley Osher, Guido Montufar. Wasserstein proximal of GANs. 4. Yifan Chen, Wuchen Li. Natural gradient in Wasserstein statistical manifold. 5. Wuchen Li, Guido Montufar. Ricci curvature for parametric statistics via optimal transport. 6. Wuchen Li. Geometry of probability simplex via optimal transport. 7. Yat-Tin Chow, Wuchen Li, Wotao Yin, Stanley Osher. Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula. 8. Shui-Nee Chow, Wuchen Li, Jun Lu, Haomin Zhou. Game theory and Discrete optimal transport. 9. Flavien Leger, Wuchen Li. Hopf-Cole transform via generalized Schrödinger bridge problem. 10. Yonatan Dukler, Wuchen Li, Alex Lin, Guido Montufar. Wasserstein of Wasserstein Loss function for learning generative models. 11. Wilfrid Gangbo, Wuchen Li, Stanley Osher, Michael Puthawala. Unnormalized optimal transport. 12. Wuchen Li, Alex Lin, Guido Montufar. Affine natural proximal learning. 13. Wuchen Li, Shu Liu, Hongyuan Zha, Haomin Zhou. Parametric Fokker-Planck equation. 14. Shui-Nee Chow, Wuchen Li, Haomin Zhou. Wasserstein Hamiltonian flows. 15. Alfredo Garbuno-Inigo, Franca Hoffmann, Wuchen Li, Andrew M Stuart. Gradient Structure Of The Ensemble Kalman Flow With Noise. Wasserstein information geometric learning, March 29, 2019, Max-Planck institute, Deep learning kickoff conference, Leipzig, Germany. Wasserstein information geometric learning, March 4, 2019, University of California, Santa Cruz. Wasserstein information geometric learning, Feb 21, 2019, Courant Institute of Mathematical Sciences, New York. Wasserstein information geometric learning, Feb 20, 2019, New Jersey Institute of Technology, New Jersey. Wasserstein information geometric learning, Optimal transport seminar, Jan 2019, Caltech. Learning via Wasserstein information geometry, Applied mathematics and Statistics Youth Forum, Dec 2018, Peking university. Mean field games and Optimal transport, Mean field games kickoff conference, Dec 2018, UCLA. Optimal transport on graph with applications, Special event, Nov 2018, University of Minnesota. Wasserstein statistical manifold, AIM conference on Restricted Boltzmann machine, Sep 2018, San Jose. Machine learning via Wasserstein statistical manifold, A first conference in Machine learning and optimal control, July 2018, Shenzhen. Dynamics in Wasserstein statistical manifold, International conference on infinite dimensional dynamical systems, Sichuan University, July 2018, Chengdu. Mean field games via probability manifold I, II, IPAM, June 2018, UCLA, Los Angeles. Wasserstein Natural gradient, Level set seminar, June 2018, UCLA, Los Angeles.
4 Wasserstein statistical manifold, Level set seminar, April 2018, UCLA, Los Angeles. Optimal transport on graphs with applications, Applied Math/PDE seminar, Feb 2018, UCSB, Santa Barbara. Optimal transport on graphs with applications, Level set seminar, Feb 2018, UCLA, Los Angeles. Schrödinger equation on graphs via optimal transport, ICMC Differential equations, Feb 2018, USP, Sao Calos, Brazil. Entropy dissipation on finite graphs, 10 to 60 conference, Dec 2017, Georgia Tech, Atlanta. Discrete Schrödinger equation via optimal transport, Nov 2017, AIMS, UC riverside. Fokker-Planck equations on finite graphs, Probability and Statistics seminar, Sep 1st, 2017, USC. Optimal control problems in density space, Level set seminar, August 29, 2017, UCLA. Dynamical system in density manifold for finite graphs, August 10, 2017, Workshop in dynamical system, Georgia Tech, Atlanta. Optimal transport with applications, June 20, 2017, Topology seminar, Chengdu. Population games via optimal transport, June 15, 2017, International Conference on Topological Nonlinear Analysis, Guangzhou. Optimal transport with Fisher information regularization, June 6, 2017, SOCAMS, UC Irvine. Discrete Schrödinger equation via optimal transport, May 6, 2017, Working Group for Problems in Transport and Related Topics in Graphs, Georgia Tech, Atlanta. Optimal transport on finite graphs with applications, March 2017, Applied math colloquium, UCLA. Optimal transport on finite graphs with applications, February 2017, Applied math seminar, Claremont Colleges. Fast algorithms for Earth Mover s distance, January 2017, Level set seminar, UCLA. Optimal transport and Entropy dissipation on finite graphs, August 29, 2016, Level set seminar, UCLA. A new model for realistic random perturbations of stochastic oscillators, July 3, 2016, AIMS Orlando conference, Orlando, Florida. A new approach to optimal control with constraints, July 1, 2016, AIMS Orlando conference, Orlando, Florida. A study of stochastic differential equations and Fokker-Planck equations with applications, April 4, 2016, Georgia Tech, Applied and computational math seminars, Atlanta, Georgia. Method of evolving junctions, 2016, University of Georgia, Athens, Georgia. Method of evolving junctions: A new approach to optimal control with constraints, April 11, 2015, SIAM student conference, Atlanta, Georgia. Newton-like algorithm for the shortest path based on the method of evolving junctions, poster section, February 28, 2015, Georgia Scientific Computing Symposium, Atlanta, Georgia.
5 Reviewers Journal of Scientific Computing; SIAM Journal of Scientific Computing; Probability and related fields; Inverse problems; Information geometry; Information and Inference: A journal of the IMA; Science report; Journal of Finance and Data Science; Taiwanese Journal of Mathematics; ICLR (International Conference on Learning Representations); Journal of Differential Equations; Geometry Science Information (co-chair); Dynamical Games and Applications; SIAM Journal of Mathematical Analysis. Conference organization Academic activities Organizer: Optimal Transport for Nonlinear Problems in ICIAM 2019, Spain. Co-chair: Wasserstein Information Geometry/Optimal Transport in Geometry Information Science (GSI) 2019, France. Mean field games, June, Los Angeles, 2017, AIMS Orlando conference, July 1-July 5, Orlando, Florida, Evolutionary Game Theory, April 27-May 1, MBI, Ohio State University, Georgia Scientific Computing Symposium, MSRI Summer school, July 07-July 18, MSRI, University of California, Berkeley, Houston Summer School, May 20-May 28, University of Houston, Research assistant, Georgia Institute of Technology, Fall 2014, Fall Supervisions of graduate student Alex Lin, UCLA, Wasserstein proximal of GANs. Jialin Liu, UCLA, Multigrid numerical scheme for Wasserstein-1 distance. Yonatan Dukler, UCLA, Wasserstein of Wasserstein loss function. Wonjun Lee, UCLA, Mean field games. Supervisions of undergraduate student Yifan Chen, Tsinghua university (now in Caltech), Bachelor s thesis: Natural gradient in Wasserstein statistical manifold.
Mean field games via probability manifold II
Mean field games via probability manifold II Wuchen Li IPAM summer school, 2018. Introduction Consider a nonlinear Schrödinger equation hi t Ψ = h2 1 2 Ψ + ΨV (x) + Ψ R d W (x, y) Ψ(y) 2 dy. The unknown
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Publications 1. With I. Kartzas and D. Ocone, An Extension of Clark s Formula, Stochastics and Stochastics Reports, Vol. 37, pp (1991).
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