Group Members and Alumni

Research group in applied and computational mathematics, with emphasis on finite element methods, porous media, data assimilation, optimal control, and scientific machine learning.

Postdoctoral Researchers

  • Dr. Kapil Chawla
    Research Associate supported by DOE Earthshot, 2025–2027
    Research topics: machine learning and multiscale methods
    • Kapil Chawla, Youngjoon Hong, Jaeyong Lee, and Sanghyun Lee, Discontinuous Galerkin finite element operator network for solving non-smooth PDEs.
    • Kapil Chawla, Sanghyun Lee, and Yeonjong Shin, A Parallel and Adaptive Mesh-Free Method for Heterogeneous Porous Media.

Graduate Students

  • Seungmin Lee
    Ph.D. student, 2023–present; supported by DOE Earthshot
    Research topics: data assimilation, porous media flow, and Biot's equation
    • Seungmin Lee and Sanghyun Lee, Convergence and Numerical Simulations of the Continuous Data Assimilation for Biot's Poroelasticity System, Computers and Mathematics with Applications, Volume 202, 15 January 2026, Pages 20–37.
  • Jonathan Valyou
    Ph.D. student, 2023–present; co-advised with Hristo Chipilski, Department of Scientific Computing; supported by DOE Earthshot
    Research topics: optimal control and data assimilation
    • Jonathan Valyou, Jeremy Brandman, and Sanghyun Lee, Optimal mean-time path planning for unmanned underwater vehicles: a Hamilton-Jacobi approach.
    • Sanghyun Lee, Zhengqi Liu, Jonathan Valyou, and Ludmil Zikatanov, A Conjugate Gradient Formulation of the EnKF Algorithm.
  • Latira Campbell
    Ph.D. student, 2023–present; co-advised with Nicholas Dexter, Department of Scientific Computing
    Research topic: graph neural networks

Group Alumni

  • Dr. SeongHee Jeong
    Postdoctoral Researcher, Department of Mathematics, 2023–2025
    Research topic: optimal control
    • SeongHee Jeong and Sanghyun Lee, Optimal Control for Darcy's Flow in a Heterogeneous Porous Medium, Applied Numerical Mathematics, Volume 207, January 2025, Pages 303–322.
  • Yi-Yung Yang
    Ph.D. student, 2021–August 2026; supported by NSF DMS-2208402, NSF DMS-2327841, and DOE Earthshot
    Research topics: enriched Galerkin methods and hyperbolic PDEs
    • Dmitri Kuzmin, Sanghyun Lee, and Yi-Yung Yang, Bound-preserving and entropy stable enriched Galerkin methods for nonlinear hyperbolic equations, Journal of Computational Physics, Volume 541, 5 November 2025, 114323.
    • Hyun-Geun Shin, Yi-Yung Yang, and Sanghyun Lee, A Posteriori Error Estimation for Parabolic Equations with Enriched Galerkin Finite Element Methods.
    • Yi-Yung Yang, Sanghyun Lee, and Dmitri Kuzmin, Heat Transfer Modeling in Enhanced Geothermal Energy: A Three-Temperature Approach for Solid, Injected, and Residing Fluids.
  • Sanjeeb Poudel
    Ph.D. student, 2022–August 2026; co-advised with Xiaoqiang Wang, Department of Scientific Computing; supported by DOE Earthshot
    Research topics: data assimilation, enriched Galerkin methods, and machine learning
    • Sanjeeb Poudel, Teeratorn Kadeethum, and Sanghyun Lee, Enhancing neural network extrapolation in thermo-fluid systems using steady-state solutions.
    • Sanjeeb Poudel, Sanghyun Lee, and Lin Mu, Pressure-robust enriched Galerkin finite element methods for coupled Navier-Stokes and heat equations.
    • Sanjeeb Poudel, Xiaoqiang Wang, and Sanghyun Lee, A novel technique for minimizing energy functional using neural networks, Engineering Applications of Artificial Intelligence, Volume 133, Part D, July 2024, 108313.
    • Ryuou Hu, Sanjeeb Poudel, Feng Bao, and Sanghyun Lee, Ensemble Score Filter for Data Assimilation of Two-Phase Flow Models in Porous Media, Journal of Computational Physics, Volume 544, 1 January 2026, 114416.
  • Ruth Lopez
    Ph.D. student, 2022–April 2026; co-advised with Feng Bao
    Research topics: ensemble score filter and data assimilation
  • Dabin Park
    Visiting Ph.D. student, 2023–2024
    Research topic: machine learning and finite element methods for inverse elliptic PDEs
    • Dabin Park, Sanghyun Lee, and Sunghwan Moon, A Machine Learning and Finite Element Framework for Inverse Elliptic PDEs via Dirichlet-to-Neumann Mapping, Journal of Computational and Applied Mathematics, Volume 486, November 2026, 117679.
NSF-DOE Geothermal INTERN student spotlight for Yi-Yung Yang

Open Positions

Undergraduate Students

Undergraduate mathematics majors enrolled in the FSU mathematics program and interested in computational and numerical mathematics research are welcome to contact me about participating in current research projects.

Graduate Students

Graduate students already enrolled in an FSU graduate program, either master's or Ph.D., and interested in our research projects can contact me directly.