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Hailiang Liu

Hailiang Liu

  • Professor of Mathematics & Computter Science
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 the mathematical theory of deep learning and PDE-based data-driven modeling.

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

In Spring 2021, I taught a new topic course:  Math 680J, Optimal transport and deep learning

Current Research Topics:

  • Deep Learning: selection dynamics for deep neural networks; fast learning algorithms; optimal transport
  • 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
  • Recovery of high frequency wave fields: Gaussian beam methods, convergence theory, level set methods for recovery
  • Kinetic theory for photon scattering: Bose-Einstein condensation phenomena in the Kompaneets model
  • Direct discontinuous Galerkin (DDG) methods: fluid equations, Fokker-Planck equations; dispersive PDEs
  • Alternating evolution (AE) methods: Hamilton-Jacobi equation, fully nonlinear PDEs

Funding Agencies