Professor Research Research Interests: Applied Math Research Interests: Approximation and mathematical control theory of partial differential equations Optimal control of transport and mixing via fluid flows Well-posedness and long-time behavior of mathematical fluid dynamics Data-driven optimal control and estimation for network dynamics Computational methods for optimal control design and model reduction Reliability of renewable systems Grants: Humboldt Research Fellowship for Experienced Researchers, 2024. 2023–2026, AFOSR, FA9550-23-1-0675, “Hybrid Control and Estimation of Semi-Dissipative Systems: Analysis, Computation, and Machine Learning”, $442,285 (single PI). 2023–2026, NSF, DMS-2229345, “Collaborative Research: AMPS: Deep-Learning-Enabled Distributed Optimization Algorithms for Stochastic Security Constrained Unit Commitment”, $320,000 (PI at UGA, $120,000), jointly with Hongyu Wu (PI at Kansas State University), and Ashesh Sinha (Co-PI at Kansas State University). 2022–2025, NSF, DMS-2205117, “Nonlinear Control and Observer Designs for Flow-Transport Systems”, $120,000 (single PI). 2021–2024, NSF, DMS-2232526, Supplemental Funding for Research Collaboration in Europe for NSF Awardees, $9,060 (PI at UGA). 2021–2024, NSF, DMS-2111486, “Collaborative Research: Computational Methods for Optino-costmal Transport via Fluid Flows”, $398,050 (PI at UGA, $145,597), jointly with John Singler (PI at Missouri S&T), Yangwen Zhang (PI at CMU). 2018–2023, NSF, DMS-2005696 (previously DMS-1813570), “Control and Optimization of Semi-Dissipative Systems”, $108,734 (single PI, no-cost extension from 2021 to 2023). Interdisciplinary Research Pre-Seed Program on “The Integration of PDE Modeling, Machine Learning and Topology Analysis in MRIs Analysis”, $3,500, UGA, 2020. 2018–2019, DARPA, HR001117S0039-Lagrange-FP-014, “Robust Optimization & Control of Dynamic Sensor Systems” $749,999 (PI at OSU, $98,000), jointly with J. Burns (PI at VT), M. Demetriou (PI at WPI), and N. Gatsonis (Co-PI at WPI). Selected Publications Selected Publications: X. Zheng, W. Hu and J. Wu, Numerical algorithms and simulations of boundary dynamic control for optimal mixing in unsteady Stokes flows, Computer Methods in Applied Mechanics and Engineering, vol. 417, Part A, 1 December 2023, 116455. doi.org/10.1016/j.cma.2023.116455. W. Hu, C. N. Rautenburg and X. Zheng, Feedback Control for Fluid Mixing via Advection, Journal of Differential Equations, 374, 2023. 126–153. doi.org/10.1016/j.jde.2023.07.009. W. Hu, Global regularity and stability analysis of the Patlak-Keller-Segel system with flow advection in a bounded domain: a semigroup approach. Nonlinear Analysis, Vol. 234, Sep. 2023, 113319. https://doi.org/10.1016/j.na.2023.113319. A. N. Ceretani, W. Hu, and C. Rautenburg, Optimal Conduit Shape for Stokes Flow, System & Control Letter, Vol. 173, Mar. 2023, 105461. doi.org/10.1016/j.sysconle.2023.105461. W. Hu, J. Liu and Z. Wang, Bilinear Control of Convection-Cooling and Computation: From Open-Loop to Closed-Loop, Applied Mathematics & Optimization, 86(5), 2022. doi.org/10.1007/s00245-022-09876-x. S. Afshar and W. Hu, Permeability Estimation of a Porous Structure based on Sampled Velocity Measurements, Inverse Problems, 38(6), 065002, 2022. W. Hu, M. A. Demetriou, X. Tian, N. A. Gatsonis, Hybrid Domain Decomposition Filters for Advection-Diffusion PDEs with Mobile Sensors, Automatica, Vol.138, April 2022, 110109. https://doi.org/10.1016/j.automatica.2021.110109. W. Gong, W. Hu, M. Mateos, J. Singler, and Y. Zhang, Analysis of an hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system, ESAIM: Mathematical Modelling and Numerical Analysis, 54(2020), 2229–2264. DOI: 10.1051/m2an/2020015. Y. Dai, W. Hu, J. Wu and B. Xiao, The Littlewood-Paley Decomposition for Periodic Functions and Applications to the Boussinesq Equations, Analysis and Applications, 18 (4), 2020, 639–682. W. Hu, J. Shen, J.Singler, Y. Zhang, and X.Zheng, A Superconvergent Hybridizable Discontinuous Galerkin Method for Dirichlet Boundary Control of Elliptic PDEs, Numerische Mathematik, 144(2), 375–411, 2020. W. Hu, An Approximating Control Design for Optimal Mixing by Stokes Flows, Applied Mathematics & Optimization, 82, 2020, 471--498. doi.org/10.1007/s00245-018-9535-4. W. Hu and J. Wu, An Approximating Approach for Boundary Control of Optimal Mixing via Navier-Stokes Flows, Journal of Differential Equations, 267(10), 2019, 5809--5850. W. Hu and J. Wu, Boundary Control for Optimal Mixing via Navier-Stokes Flows, SIAM Journal on Control and Optimization, 56(4), 2018, 2768--2801. W. Gong, W. Hu, M. Mateos, J. Singler, X. Zhang, and Y. Zhang, A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity, SIAM Journal on Numerical Analysis, 56(4), 2018, 2262--2287. Teaching Teaching: Ph.D., Mathematics, Virginia Tech.
