Sanghyun Lee

Generalized Multiscale Enriched Galerkin Method for Flow in Heterogeneous Porous Media
Mathematical Models and Methods in Applied Sciences. https://doi.org/10.1142/S0218202526500570

Adaptive matrix-free simulations of fluid-filled phase-field fractures with fixed-stress coupling and fracture-width computation
International Journal for Numerical Methods in Engineering 127, no. 15 (2026): e70392, https://doi.org/10.1002/nme.70392.

Presented in the Department of Mathematics Seminar

Presented in Prof. Youngjoon Hong's research group, Machine Learning and Scientific Computing (MLSC) LAB link

Presented in Prof. Baehyun Min's research group, Energy systems laboratory link

The project title is "AI-Powered Manufacturing of High Temperature Superconductors for Fusion Energy" and tackles the challenge area: Reenvisioning Advanced Manufacturing and Industrial Productivity. The following is from the link FSU NEWS.
Led by Associate Professor Fumitake Kametani, this project uses AI to transform how high temperature superconducting tapes are made for fusion energy magnets. Manufacturing these highly engineered tapes involves subtle, hard-to-detect variations that limit performance uniformity and thus drive up costs of magnets, so the team is building an AI “digital twin”, which is a predictive computer model of the production line. This model learns how manufacturing conditions shape tape quality, helping rebuild a US-owned supply chain of this critically important technology for US energy security. FSU leads the project with the US manufacturer High Temperature Superconductors, Inc., and Lawrence Berkeley National Laboratory. Sanghyun Lee, associate professor of Mathematics, and National High Magnetic Field Laboratory researchers Aixia Xu, Yan Xin, Jeseok Bang, and Chris Segal, will also play key roles in executing the project, as well as MagLab Chief Materials Scientist David Larbalestier.

The project title "Operator-CompositionBased Theoretical Analysis of Deep Neural Networks: Focusing on the Transformer(the Core Architecture of LLM)" got funded through Basic Science Research Program / Basic Research Lab (BRL) by Ministry of Science and ICT / National Research Foundation in South Korea. This project is for three years and the PI is Prof. Sunghwan Moon from Kyoungbook National University.

Title: Physics-Preserving Enriched Galerkin Methods for Hyperbolic and Coupled Flow–Transport Problems

Local conservation, maximum-principle preservation, and entropy stability are crucial for producing physically meaningful numerical simulations of hyperbolic and coupled flow–transport problems. In this dissertation, we develop physics-preserving enriched Galerkin finite element methods for these problems. We first study coupled Darcy flow and linear transport problems in porous media, where locally conservative enriched Galerkin flow discretizations are used to provide reliable velocity fields for transport simulations. To prevent nonphysical undershoots and overshoots, we incorporate flux-corrected transport techniques into the enriched Galerkin framework so that the numerical concentration satisfies a discrete maximum principle. Next, we study nonlinear scalar hyperbolic conservation laws, for which weak solutions may not be unique and entropy stability is needed to select the physically admissible solution. To address this issue, we develop bound-preserving and entropy-stable enriched Galerkin schemes by using algebraic flux correction and monolithic convex limiting techniques. Finally, we apply the proposed framework to enhanced geothermal energy modeling and develop a three-temperature local thermal nonequilibrium model that distinguishes the thermal behavior of injected fluid, resident fluid, and the solid matrix. Numerical experiments validate the proposed methods for locally conservative flow, bound-preserving transport, entropy-stable nonlinear conservation laws, and geothermal flow and heat-transfer simulations.

Postdoc Dr. K. Chawla and Ph.D. student Y. Yang presented their work.

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.

Postdoc Dr. K. Chawla and Ph.D. students S. M. Lee, J. Valyou, and Y. Yang presented their work.

The paper is co-authored with Jihoon Kim and Mary Wheeler, and the title is The von Neumann Stability Analysis of the Fixed-Stress Schemes in Poroelastodynamics.

The paper is co-authored with Seungmin Lee, and the title is Convergence and Numerical Simulations of the Continuous Data Assimilation for Biot’s Poroelasticity.

The paper is co-authored with Hemanta Kunwar and Son-Young Yi, and the title is Non-intrusive Global-local Method for Poroelasticity Problems with Localized Pressure Effects.

The program is available here: Program.

The program is available here: Program.

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 version is available below.

The paper is co-authored with Yi-Yung Yang and Dmitri Kuzmin (TU Dortmund), and it is titled Bound-preserving and Entropy Stable Enriched Galerkin Methods for Nonlinear Hyperbolic Equations. The arXiv version is available below.

The participant list and photo are available here: link.
The title of the talk was Bound-preserving and Entropy Stable Enriched Galerkin Methods for Nonlinear Hyperbolic Equations.

Kapil Chawla received his Ph.D. from Indiana University in 2025. His Ph.D. advisor is R. Temam. Kapil is funded by the DOE Earthshot program and will work on machine-learning-based multiscale methods. Welcome!