Honghu Liu

Department of Mathematics
Virginia Tech

Office: 468 McBryde Hall
Phone: (540) 231-7249
E-mail: hhliu@vt.edu

Mailing address:
460 McBryde Hall, Virginia Tech
225 Stanger Street
Blacksburg, VA 24061-0123

Research interests

My current research focuses on the following areas:

  • Deterministic/Random Dynamical Systems
  • Model Reductions, Stochastic Parameterization
  • Optimal Control
  • Fluid Dynamics
  • Bifurcation Analysis and Phase Transition

Publications

Monographs

  1. Mickaël D. Chekroun, Honghu Liu & Shouhong Wang. Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations: Stochastic Manifolds for Nonlinear SPDEs II. SpringerBriefs in Mathematics. Springer, New York, xvii+129 pp., 2015. [Springer link] [see also the Preprint]
  2. Mickaël D. Chekroun, Honghu Liu & Shouhong Wang. Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I. SpringerBriefs in Mathematics. Springer, New York, xv+127 pp., 2015. [Springer link] [see also the Preprint]

Book chapters

  1. William Snyder, Changhong Mou, Honghu Liu, Omer San, Raffaella De Vita & Traian Iliescu. Reduced Order Model Closures: A Brief Tutorial. In Recent Advances in Mechanics and Fluid-Structure Interaction with Applications, Edited by F. Carapau and A. Vaidya, Birkhäuser, 167–193, 2022. [Publication link] [Preprint]
  2. Mickaël D. Chekroun & Honghu Liu. Optimal management of harvested population at the edge of extinction. In Advances in Nonlinear Biological Systems: Modeling and Optimal Control, Edited by J. Kotas, American Institute of Mathematical Sciences, Chapter 2, 35–72, 2020. [Publication link] [Preprint]
  3. Mickaël D. Chekroun, Axel Kröner & Honghu Liu. Galerkin approximations for the optimal control of nonlinear delay differential equations. In Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal Control, Edited by Dante Kalise, Karl Kunisch and Zhiping Rao, De Gruyter, Berlin, Boston, Chapter 4, 61–96, 2018. [Publication link] [Preprint]

Research articles

  1. Mickaël D. Chekroun, Honghu Liu, James C. McWilliams & Shouhong Wang. Transitions in stochastic non-equilibrium systems: Efficient reduction and analysis. Journal of Differential Equations, 346, 145-204, 2023. [Journal link]
  2. Matthias Chung, Justin Krueger & Honghu Liu. Least-squares finite element method for ordinary differential equations. Journal of Computational and Applied Mathematics, 418, 114660, 2023. [Journal link] [Preprint]
  3. Mickaël D. Chekroun, Ilan Koren, Honghu Liu & Huan Liu. Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations. Science Advances, 8, eabq7137, 19 pp., 2022. [Journal link]
  4. Birgul Koc, Changhong Mou, Honghu Liu, Zhu Wang, Gianluigi Rozza & Traian Iliescu. Verifiability of the data-driven variational multiscale reduced order model. Journal of Scientific Computing, 93, Article number: 54, 26 pp., 2022. [Journal link]
  5. Nan Chen, Yingda Li & Honghu Liu. Conditional Gaussian nonlinear system: a fast preconditioner and a cheap surrogate model for complex nonlinear systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32, 053122, 30 pp., 2022. [Journal link]
  6. Nan Chen, Honghu Liu & Fei Lu. Shock trace prediction by reduced models for viscous stochastic Burgers equations. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32, 043109, 17 pp., 2022. [Journal link]
  7. Mickaël D. Chekroun, Honghu Liu & James C. McWilliams. Stochastic rectification of fast oscillations on slow manifold closures. Proceedings of the National Academy of Sciences, 118, e2113650118, 2021. [Journal link]
  8. Mickaël D. Chekroun, Ilan Koren & Honghu Liu. Efficient reduction for diagnosing Hopf bifurcation in delay differential systems: Applications to cloud-rain models. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30, 053130, 2020. [Journal link]
  9. Mickaël D. Chekroun, Honghu Liu & James C. McWilliams. Variational approach to closure of nonlinear dynamical systems: Autonomous case. Journal of Statistical Physics, 179, 1073–1160, 2020. [Journal link] [Preprint]
  10. Changhong Mou, Honghu Liu, David R. Wells & Traian Iliescu. Data-driven correction reduced order models for the quasi-geostrophic equations: A numerical investigation. International Journal of Computational Fluid Dynamics, 34, 147–159, 2020. [Journal link] [Preprint]
  11. Traian Iliescu, Honghu Liu & Xuping Xie. Regularized Reduced Order Models for a Stochastic Burgers Equation. International Journal of Numerical Analysis & Modeling, 15, 594–607, 2018. [Journal link] [Preprint]
  12. Niklas Boers, Mickaël D. Chekroun, Honghu Liu, Dmitri Kondrashov, Denis-Didier Rousseau, Anders Svensson, Matthias Bigler & Michael Ghil. Inverse stochastic-dynamic models for high-resolution Greenland ice-core records. Earth System Dynamics, 8, 1171–1190, 2017. [Journal link]
  13. Mickaël D. Chekroun, Axel Kröner & Honghu Liu. Galerkin approximations of nonlinear optimal control problems in Hilbert spaces. Electronic Journal of Differential Equations, 2017, No. 189, 1–40, 2017. [Journal link] [Preprint]
  14. Mickaël D. Chekroun, Honghu Liu & James C. McWilliams. The emergence of fast oscillations in a reduced Primitive Equation model and its implications for closure theories. Computers and Fluids, 151, 3–22, 2017. [Journal link] [Preprint]
  15. Mickaël D. Chekroun & Honghu Liu. Post-processing finite-horizon parameterizing manifolds for optimal control of nonlinear parabolic PDEs. Proceedings of 55th IEEE Conference on Decision and Control (CDC), 2016. [Journal link]
  16. Mickaël D. Chekroun, Michael Ghil, Honghu Liu & Shouhong Wang. Low-dimensional Galerkin approximations of nonlinear delay differential equations. Disc. Cont. Dyn. Sys. A, 36, 4133–4177, 2016. [Journal link] [Preprint]
  17. Mickaël D. Chekroun & Honghu Liu. Finite-horizon parameterizing manifolds, and applications to suboptimal control of nonlinear parabolic PDEs. Acta Appl. Math., 135, pp 81–144, 2015. [Journal link]
  18. Honghu Liu, Taylan Sengul, Shouhong Wang & Pingwen Zhang. Dynamic transitions and pattern formations for a Cahn-Hilliard model with long-range repulsive interactions. Comm. Math. Sci., 13, pp 1289–1315, 2015. [Journal link]
  19. Honghu Liu, Taylan Sengul & Shouhong Wang. Dynamic transitions for quasilinear systems and Cahn-Hilliard equation with Onsager mobility, J. Math. Phys., 53:023518, 33 pp., 2012. [Journal link]
  20. Honghu Liu. Phase transitions of a phase field model, Disc. Cont. Dyn. Sys. B, 16, 883–894, 2011. [Journal link]

Preprints and Articles under review

  1. Mickaël D. Chekroun, Honghu Liu & Shouhong Wang. Non-Markovian reduced systems for stochastic partial differential equations: The additive noise case. Preprint, arXiv:1311.3069, 11 pp., 2013.
  2. Mickaël D. Chekroun, Honghu Liu & Shouhong Wang. On stochastic parameterizing manifolds: Pullback characterization and Non-Markovian reduced equations. Preprint, arXiv:1310.3896, 143 pp., 2013.

 

Last modified on 12/09/2022.