Hailiang Liu

Hailiang Liu

  • Professor of Mathematics
  • Professor of Computer Science (by courtesy)
  • NSF Program Director
  • Member, Translational AI Center (TrAC)
  • Data Science/AI Coordinator (Dept. of Math)
Effective April 8, 2024, I serve on detail as a program director in the division of Mathematical Sciences (MPS/DMS) at the National Science Foundation (NSF).

I am a Professor at the Department of Mathematics, Iowa State University, specializing in Computational and Applied Mathematics. My research spans several areas, including mathematical modeling through partial differential equations (PDEs), applied analysis, numerical methods, and scientific computing. Currently, I am exploring the intersection of mathematical foundations with emerging technologies such as deep learning, as well as leveraging data-driven approaches to address PDE-based problems.


Contact Info

434 Carver
411 Morrill Rd.
Social Media and Websites


  • 1995, Ph.D. Applied Math, Chinese Academy of Sciences
  • 1988, M.Sc. Applied Math, Tsinghua University
  • 1984, B.Sc. Math Education, Henan Normal University

Current Research Topics:

  • Deep Learning: selection dynamics for deep neural networks; fast learning algorithms; optimal transport for density estimatie
                               Data-driven optimal control modeling using deep neural networks. 
  • Mathematical Biology: selection dynamics in population evolution; Evolution in biased dispersal in Ecology; aggregation,
                                          population balance
  • Critical threshold analysis: Hyperbolic balance laws and related models
  • Kinetic theory for photon scattering: Bose-Einstein condensation phenomena in the Kompaneets model
  • Recovery of high frequency wave fields: Gaussian beam methods, convergence theory, level set methods for recovery
  • Direct discontinuous Galerkin (DDG) methods: fluid equations, Fokker-Planck equations; dispersive PDEs
  • Alternating evolution (AE) methods: Hamilton-Jacobi equation, fully nonlinear PDEs

Funding Agencies