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
    Publication List:
    • Kapil Chawla, Sanghyun Lee, Jonathan Valyou A Hybrid Coarse-to-Fine Framework for Quantum Computing in Heterogeneous Darcy Flow.
    • Kapil Chawla, Sanghyun Lee, Yeonjong Shin A Parallel and Adaptive Mesh-Free method for Heterogeneous Porous Medias.
    • Kapil Chawla, Youngjoon Hong, Jaeyong Lee, and Sanghyun Lee, Discontinuous Galerkin finite element operator network for solving non-smooth PDEs.

Graduate Students

  • Latira Campbell
    Ph.D. student, 2023–present; co-advised with Nicholas Dexter, Department of Scientific Computing
    Research topic: Sampling, Scientific Machine Learning, Graph Neural Networks
  • Seungmin Lee
    Ph.D. student, 2023–present; supported by DOE Earthshot; article about Geothermal INTERN link
    Intern: Lawrence Livermore National Lab
    Research topics: data assimilation, porous media flow, and Biot's equation
    Publication list:
    • Seungmin Lee, Chen Liu, Sanghyun Lee, Optimization-based Cell Average Limiters as Metric Projections: Constrained Evolution and Convergence Analysis for Convection-diffusion Equations
    • Seungmin Lee, Sanghyun Lee, Chen Liu, An optimization-based property-preserving limiter for two-phase flow in porous media on non-matching meshes
    • 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
    Intern: U.S. Naval Research Laboratory (2023), Sandia National Lab (2026)
    Research topics: optimal control and data assimilation
    Publication list:
    • Kapil Chawla, Sanghyun Lee, Jonathan Valyou A Hybrid Coarse-to-Fine Framework for Quantum Computing in Heterogeneous Darcy Flow.
    • 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.
  • Thomas Kuiper
    Ph.D. student, 2025–present;
    Research Topics: Magnetostatistics, Elasticity, and Fractures

Group Alumni

  • Dr. SeongHee Jeong
    Postdoctoral Researcher, Department of Mathematics, 2023–2025
    Research topic: optimal control
    • Seonghee Jeong, Sanghyun Lee, A Monolithic Discontinuous Galerkin Framework for Darcy Optimal Control with Radon-Measure Tracking and Pointwise Control Constraints, 2026
    • 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
    Intern: Sandia National Lab
    Research topics: enriched Galerkin methods and hyperbolic PDEs
    Thesis title: Physics-Preserving Enriched Galerkin Methods for Hyperbolic and Coupled Flow-Transport Problems
    Publication list:
    • 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.
    NSF-DOE Geothermal INTERN student spotlight for Yi-Yung Yang
  • 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
    Thesis title: Enhancing Fluid and Thermal Simulations: Integrating Finite Element Method, Scientific Machine Learning, and Data Assimilation
    First Job Placement: Postdoctoral Scholar, The Pennsylvania State Univeresity
    Publication list:
    • 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 Yolibeth Lopez Fajardo
    Ph.D. student, 2022–April 2026; co-advised with Feng Bao
    Research topics: ensemble score filter and data assimilation
    Thesis title: Model-Data Integration in Complex Dynamical Systems: Applications in Materials Synthesis
    First Job Placement: Quantitative Analyst, Wells Fargo

Visiting Ph.D Students

  • 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.

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.