Portrait of Sanghyun Lee

Sanghyun Lee, Ph.D.

Associate Professor, Department of Mathematics, Florida State University
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Contact

Appointments

  • Fall 2023 - Associate Professor, Department of Mathematics, Florida State University
  • Spring 2024 Associate of Data Science, Florida State University [link]
  • Spring 2018 Associate of Geophysical Fluid Dynamics Institute, Florida State University [link]
  • Fall 2017 Assistant Professor, Department of Mathematics, Florida State University

Useful Links

News

2026
Paper A joint paper with S. Moon and D. Park got accepted at JCAM
A Machine Learning and Finite Element Framework for Inverse Elliptic PDEs via Dirichlet-to-Neumann Mapping D. Park, S. Lee, S. Moon, Journal of Computational and Applied Mathematics
Presentation Lee's group presented at the 4th Southeast ACM Student Workshop
Postdoc Dr. K. Chawla, and Ph.D. students SM Lee, J. Valyou, and Y. Yang presented their work.
Presentation Lee presented at FSU-NC PDE Workshop
Presentation Lee presents at NACS Seminar, Rice University
2025
Presentation Lee presented at ARAMCO
Paper Our paper is now accepted for publication in International Journal for Numerical and Analytical Methods in Geomechanics
The paper is co-authored with Jihoon Kim and Mary Wheeler, and the title of the paper is The von Neumann Stability Analysis of the Fixed-Stress Schemes in Poroelastodynamics
Paper Our paper is now accepted for publication in Computers and Mathematics with Applications.
The paper is co-authored with Seungmin Lee, and the title of the paper is Convergence and Numerical Simulations of the Continuous Data Assimilation for Biot’s Poroelasticity
Paper Our paper is now accepted for publication in International Journal for Numerical and Analytical Methods in Geomechanics
The paper is co-authored with Hemanta Kunwar and Son-Young Yi, and the title of the paper is Non-intrusive global-local method for poroelasticity problems with localized pressure effects.
Presentation Lee presented a talk at ARMA Hydrualic Fracturing Seminar
Presentation Lee presented a talk at CCAM Purdue University, Indiana
Organizer/Presentation Lee co-chaired to orgainze a minisymposium at SIAM GeoScience Conference in LSU. Also, presented a talk
Organizer/Presentation Lee co-chaired to orgainze 8th Biot Conference in Utah. Also, presented a talk
The program of this conference is provided in this link Program
Presentation Kapil Chawla and Jonathan Valyou presented in 12th Graduate Student Conference at Clemson University
The program of this conference is provided in this link Program
Paper Our paper is now accepted for publication in Journal of Compuational Physics
The paper is co-authored with Ryuou Hu, Sanjeeb Poudel, and Feng Bao from Florida State University, and it is titled Ensemble Score Filter for Data Assimilation of Two-Phase Flow Models in Porous Media The arXiv is provided in below link
arXiv
Paper Our paper is now accepted for publication in Journal of Compuational Physics
The paper is co-authored with Yi-Yung Yang and Dmitri Kuzmin (TU Dortmnud), and it is titled Bound-preserving and entropy stable enriched Galerkin methods for nonlinear hyperbolic equations. The arXiv is provided in below link
arXiv
Earlier 2025
Presentation Lee presented a Talk at MoST 2025 - Moselle Vally, Germany
The list of the participants and the photo is here link
The title of my talk was Bound-preserving and entropy stable enriched Galerkin methods for nonlinear hyperbolic equations
Slides (PDF) Abstract
New Member Kapil Chawla joined our group at FSU
Kapil Chawla has his Ph.D from Indiana University (2025). His Ph.D advisor is R. Temam. Kapil is funded by the DOE Earthshot program and will be working on developing machine learning based multi scale methods. Welcome!

Funded Projects

Active
  • Department of Energy DOE Science Foundations for the Energy Earthshots 10/2023-09/2026
    DE-SC0024703
    Advanced Multi-Physics Machine Learning for Subsurface Energy Systems Across Scales
    PI: University of Texas at El Paso; Co-PIs: Florida State University, Sandia National Labs, University of Utah
    DOE site
  • National Science Foundation National Science Foundation DMS 09/2024 - 08/2027
    NSF #2349382
    REU Site: Applied Mathematics in Real World Problems
    Senior Personel: lead project Data Assimilation and Parameter Prediction Algorithms for Subsurface Flows and simplified models in Fluid Dynamics
    Link-Webpage, NSF Web
Completed
  • National Science Foundation National Science Foundation DMS 06/2024 - 05/2025
    Supplemental: Geothermal INTERN DMS-2419267
    Dear Colleague Letter: Non-Academic Research Internships for Graduate Students in Geothermal Energy
    Seungmin Lee visited Lawrence Livermore National Lab (Dr. Joshua White)
    DOE article
  • National Science Foundation National Science Foundation DMS 06/2023-05/2024
    Supplemental: Geothermal INTERN DMS-2327841
    Dear Colleague Letter: Non-Academic Research Internships for Graduate Students in Geothermal Energy
    Yi-Yung Yang; Sandia National Lab (Dr. Hongkyu Yoon)
    DOE article
  • National Science Foundation National Science Foundation DMS 06/2022-06/2025
    Collaborative Research: DMS-2208402
    Physics-Preserving Adaptive Finite Element Methods for Thermo-Poroelasticity
    PI: Sanghyun Lee (collaborate PI: Son-Young Yi; The University of Texas at El Paso)
    NSF link
  • National Science Foundation National Science Foundation DMS 08/2019-07/2022
    DMS-1913016
    Fluid-filled Fracture Propagation with a Phase-Field Approach in Subsurface by Employing Nonlinear Strain-Limiting Models and Enriched Galerkin Methods
    PI: Sanghyun Lee
    NSF link
  • Florida State University Multidisciplinary Support 2020-2021
    MDS: #045490
    Studies for Degradation of Lignin-based Biodegradable Plastics to Prevent Marine Debris
    CRC link
  • Florida State University First Year Assistant Program (FYAP) 05/2018 - 08/2018
    CRC: 041950
    Optimal Error Estimate of Flow Problems with Dirac Sources in Subsurface for Discontinuous and Enriched Galerkin Methods




Upcoming Workshops/Conferences/Talks/Events

2026
2025
  • 26-28 Sep 2025
    Texas-Louisiana Section of SIAM - 8th Annual Meeting
    Austin, Texas
  • 7-10 Oct 2025 Main Organizer
    8th Biot Conference on Poromechanics (BIOT-8)
    Salt Lake City, Utah, USA link
  • 14-17 Oct 2025 MS Organizer
    SIAM Conference on Mathematical & Computational Issues in the Geosciences (GS25)
    Baton Rouge, Louisiana, USA link
  • 20th Oct 2025
    Applied Math Seminar
    Purdue University, USA
  • 30th Oct 2025
    Hydraulic Fracturing Seminar
    ARMA
  • 3-7 Mar 2025
    SIAM Conference on Computational Science and Engineering (CSE25)
    Dallas, Texas
  • 4-5 Apr 2025
    Southeast Applied & Computational Math Student Workshop
    Auburn University, Alabama, link
  • 8-9 May 2025
    NSF Comp Math Meeting
    The University of Utah, Utah
  • 15-16 May 2025
    DOE EarthShot PI Meeting
    The University of Texas at El Paso, El Paso, Texas
  • 19-22 May 2025
    17th Annual International Conference on Porous Media
    Albuquerque, New Mexico, USA- Organize: MS07 here
  • 27-31 Jul 2025
    Modeling and Simulation of Transport Phenomena (MoST)
    Moselle Valley, Germany, link
2024
  • 12-16 Feb 2024
    ICERM: Numerical Analysis of Multiphysics Problems
    Brown University, Providence, link
  • 21 Mar 2024
    Affiliates Meeting
    The Center for Subsurface Modeling, UT Austin
  • 23-24 Mar 2024
    AMS Spring Southeastern Sectional Meeting
    Florida State University, link - FSU news
  • 5-7 Apr 2024
    Southeast Applied & Computational Math Student Workshop
    Georgia Institute of Technology, link
  • 20-21 Apr 2024
    The Eleventh Graduate Student Conference
    Clemson
  • 12 Apr 2024
    Machine Learning Seminar
    Department of Mathematics, Florida State University
  • May 2024
    Visiting
    Leibniz University Hannover, Germany
  • 14 May 2024
    Seminar
    Dortmund, Germany
  • 15 May 2024
    Seminar, Institut fur Baumechanik und Numerische Mechanik (IBNM)
    Leibniz University Hannover, Germany
  • 16 May 2024
    Seminar, Institute of Applied Mathematics
    Leibniz University Hannover, Germany
  • 8-12 Jul 2024
    SIAM Annual Meeting
    Spokane, Washington, link
  • 15-16 Jul 2024
    NSF PI Meeting
    Seattle, Washington
  • 21-26 Jul 2024
    WCCM & PACAM
    Vancouver, BC, Canada, link
  • 11-16 Aug 2024
    11th deal.II Workshop
    Colorado State University, Fort Collins, Colorado (link)
  • 19 Sep 2024
    Yonsei University
    Seoul, South Korea
  • 26-27 Sep 2024
    Kyungpook National University
    Daegu, South Korea
  • 11-13 Oct 2024
    SIAM Texas-Louisiana Section, 7th Annual Meeting
    Baylor University, link
  • 21-25 Oct 2024
    SIAM Conference on Mathematics of Data Science (MDS24)
    Atlanta, U.S.A, link
  • 14 Nov - 3 Dec 2024
    Technical University of Dortmund
    Germany




Research Team

Research Interests

  • Design, analysis, and implementation of numerical methods for partial differential equations.
  • Computational mathematics with high-performance computing for interdisciplinary multi-physics and multi-scale real-world problems. In particular, focus on subsurface applications.
  • Free-boundary multiphase problems using projection methods for Navier-Stokes and level set methods with adaptive finite elements. Video
  • Analysis and computation of physics preserving (local mass conservation, locking free, maximum principle, and so on) enriched Galerkin methods for coupling flow and transport in porous media.
  • Multi physical and multi scale problems in porous pedia, including fracture systems; phase-field fracture with Biot thermo-hydro-mechanic-chemical coupling.
  • Employing machine learning / deep learning / neural networks for solving inverse problems, and data assimilation problems based on physical partial differential equations.