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Genming Bai

Postdoctoral Assistant Professor
Department of Mathematics, University of Michigan
Ann Arbor, Michigan, USA
E-mail: gbai AT umich.edu, genming.bai AT connect.polyu.hk, gbai AT pku.edu.cn

About me

I am currently a postdoctoral assistant professor at University of Michigan working on applied and computational mathematics. I obtained my PhD degree from The Hong Kong Polytechnic University (PolyU) (2022--2023). Prior to that I obtained a master degree in CSE (robotics track) and a bachelor degree in Physics from ETH Zürich and Peking University respectively.

Research interests

  • Numerical methods and analysis for linear and nonlinear PDEs

  • Structure preserving algorithms

  • High-performance computing and mathematical software

  • Quantum computing and scientific machine learning

Employment

Postdoctoral Assistant Professor
Department of Mathematics, University of Michigan, Ann Arbor, 2024--current

Postdoctoral Fellow
Department of Applied Mathematics, The Hong Kong Polytechnic University, 2023--2024

Education

Ph.D. in Applied Mathematics, The Hong Kong Polytechnic University, 2022--2023

M.Sc. in Computational Science and Engineering, ETH Zürich, 2018--2021

B.Sc. in Physics, Peking University, 2014--2018

Awards

Faculty of Science Outstanding PhD Thesis Awards (Link), HK PolyU, Sept. 2024

The Hong Kong Mathematical Society (HKMS) Best Thesis Award (Link), May 2024

Silver Medal, the 30th Chinese Physics Olympiad (CPHO) (Link), Nov. 2013

Publications

  1. G. Bai, H. Garcke, B. Li and S. Veerapaneni. On the convergence of the BGN method of transport type. In preparation.

  2. G. Bai, B. Li, and Y. Xie. Optimal trajectory-wise L2 convergence of Dzuik's method for mean curvature flow. In preparation.

  3. G. Bai, B. Li and S. Veerapaneni. Simulation of inextensible vesicles with tangential smoothing. In preparation.

  4. G. Bai, B. Li, and Y. Xie. Convergence of BGN-type method for surface diffusion. To be submitted.

  5. G. Bai, J. Cui, and B. Li. Discrete stochastic maximal Lp-Lq regularity of semi-discrete finite element methods. Submitted.

  6. G. Bai, B. Kovács, and B. Li. Maximal regularity of parametric finite element method for parabolic equations on evolving surfaces. Submitted.

  7. G. Bai, D. Leykekhman, and B. Li. Weak maximum principle of finite element methods for parabolic equations in polygonal domains. Submitted.

  8. G. Bai, X. Gui, and B. Li. Convergence of multistep projection methods for harmonic map heat flows into general surfaces. Submitted.

  9. G. Bai and B. Li. Convergence of parametric finite element methods of the Barrett–Garcke–Nürnberg type for curve shortening flow. Mathematics of Computation, 2024 (70 pages). doi: 10.1090/mcom/4019

  10. G. Bai, J. Hu, and B. Li. A convergent evolving finite element method with artificial tangential motion for surface evolution under a prescribed velocity field. SIAM Journal on Numerical Analysis, 2024. doi: 10.1137/23M156968X

  11. G. Bai, J. Hu, and B. Li. Arbitrary high-order mass and energy conserving methods for the Schrödinger equation. SIAM Journal on Scientific Computing, 2024. doi: 10.1137/22M152178X

  12. G. Bai and B. Li. A new approach to the analysis of parametric finite element approximation to mean curvature flow. Foundations of Computational Mathematics, 2023 (65 pages). doi: 10.1007/s10208-023-09622-x

  13. G. Bai and B. Li. Erratum: Convergence of Dziuk’s semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements. SIAM Journal on Numerical Analysis, 2023. doi: 10.1137/22M1521791

  14. G. Bai, B. Li and Y. Wu. A constructive low-regularity integrator for the one-dimensional cubic nonlinear Schrödinger equation under Neumann boundary condition. IMA Journal of Numerical Analysis, 2022. doi: 10.1093/imanum/drac075

  15. G. Bai, U. Koley, S. Mishra, and R. Molinaro. Physics Informed Neural Networks (PINNs) for approximating nonlinear dispersive PDEs. Journal of Computational Mathematics, 2021. doi: 10.4208/jcm.2101-m2020-0342

Preprints available upon request.

Teaching

Introduction to Numerical Methods (MATH 471), UMICH, Spring 2025

Calculus II (MATH 116), UMICH, Autumn 2024

Statistical Machine Learning (tutorial course), HK PolyU, Autumn 2023

Teaching assitant for Mathematics I, HK PolyU, Spring 2023

Teaching assitant for Mathematics for Engineers, HK PolyU, Autumn 2022

Teaching assitant for Basic Mathematics II - Calculus and Linear Algebra, HK PolyU, Spring 2022

Student coding assitant for Numerical Methods for CSE, ETH, Autumn 2020


A brief cv.