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Hailiang Liu

Hailiang Liu

  • Professor of Mathematics
  • Professor of Computer Science (by courtesy)
  • Member, Translation AI Center (TrAC)
  • Data Science/AI Coordinator, Department of Mathematics
I am a Professor at the Department of Mathematics, Iowa State University. I work in a number of areas in Computational and Applied Mathematics, with research interests in the interplay of mathematical modeling of application problems by partial differential equations (PDEs), applied analysis, numerical methods, and scientific computing. My current work focuses on mathematical foundations for deep learning and data-driven methods for PDE-based problems.

Contact Info

434 Carver
411 Morrill Rd.


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

More Information

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