Research

Research Interests: Numerical Analysis and Scientific Machine Learning

My research primarily focuses on the numerical methods for nonlinear PDEs and the underlying theoretical analysis. In particular, I am interested in finite element methods and scientific machine learning, including their rigorous convergence analysis. By integrating theoretical insights with computational practice, my work seeks meaningful connections between pure mathematics and applied computation from an interdisciplinary perspective.

• Numerical analysis of PDEs: finite element methods and underlying PDE analysis

• Scientific machine learning: machine-learning methods for PDEs with convergence analysis

Publications & Preprints

Numerical Analysis

• Quasi-Monte Carlo finite element approximation of the Navier-Stokes equations with initial data modeled by log-normal random fields

Seungchan Ko, Guanglian Li and Yi Yu, International Journal for Uncertainty Quantification (accepted for publication), (2025).

• Error analysis for a fully-discrete finite element approximation of the unsteady p(⋅,⋅)-Stokes equations 

Luigi C. Berselli and Alex Kaltenbach,  arXiv:2501.00849 [math.NA], submitted (2025). 

• Finite element approximation of steady flows of generalized Newtonian fluids with concentration-dependent power-law index

Seungchan Ko and Endre Suli,  Mathematics of Computation, Volume 88(317): 1061-1090 (2019).

• Finite element approximation of an incompressible chemically reacting non-Newtonian fluid

Seungchan Ko, Petra Pustejovska and Endre Suli,  ESAIM: M2AN, Volume 52 509–541 (2018).

Scientific Machine Learning

• Locking-Free Training of Physics-Informed Neural Network for Solving Nearly Incompressible Elasticity Equations

Josef Dick, Seungchan Ko, Kassem Mustapha and Sanghyeon Park, arXiv:2505.21994 [math.NA], submitted (2025).

• VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior 

Seungchan Ko and Sang Hyeon Park,  J. Comput. Phys. Volume 529, 113860  (2025).

• Finite Element Operator Network for Solving Elliptic-Type Parametric PDEs

Youngjoon Hong, Jae Yong Lee and Seungchan Ko SIAM J. Sci. Comput.  Vol. 47, Iss. 2 (2025).

• Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs

Youngjoon Hong, Jae Yong Lee and Seungchan Ko, arXiv:2404.17868 [math.NA], submitted (2024).

• Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs

Youngjoon Hong, Seungchan Ko and Seok-Bae Yun, arXiv:2211.08900 [math.NA], submitted (2023).

PDE Analysis

• On the local well-posedness of strong solutions to the unsteady flows of shear-thinning non-Newtonian fluids with a concentration-dependent power-law index

Kyueon Choi, Kyungkeun Kang and Seungchan Ko arXiv:2505.05152 [math.AP], submitted (2025).

• Some Liouville-type theorems for the stationary 3D magneto-micropolar fluids

Jae-Myoung Kim and Seungchan Ko, Acta Math. Sci.  Volume 44, pages 2296–2306  (2024).

• On the existence of strong solutions for unsteady motions of incompressible chemically reacting generalized Newtonian fluids

Kyueon Choi, Kyungkeun Kang and Seungchan Ko, arXiv:2407.05628 [math.AP], submitted (2024).

• Upper and lower bounds of convergence rates for strong solutions of the generalized Newtonian fluids with non-standard growth conditions 

Jae-Myoung Kim and Seungchan Ko,  Z. Angew. Math. Phys. 73 (251),  (2022).

• Temporal decay of strong solutions for generalized Newtonian fluids with variable power-law index,

Seungchan Ko, J. Math. Phys. Volume 63(4), (2022).

• Existence of global weak solutions for unsteady motions of incompressible chemically reacting generalized Newtonian fluids,

Seungchan Ko, J. Math. Anal. Appl. Volume 513(1) (2022).

Engineering Applications

• Engineering application of physics-informed neural networks for Saint-Venant's torsion

Su Yeong Jo, Seungchan Ko, Sanghyeon Park,  Jongcheon Park, Hosung Kim, Sangseung Lee and Joongoo Jeon, arXiv:2505.12389 [cs.LG], submitted (2025).

• A novel approach for wafer defect pattern classification based on topological data analysis

Seungchan Ko and Dowan Koo,  Expert Systems with Applications, 120765, (2023). 

Finite Element Operator Network (FEONet)

Project Page: https://2jaeyong.github.io/FEONet_project/

Code: https://github.com/2JaeYong/FEONet_project