Research

Research Interests

My primary research interests are in machine learning, numerical analysis, and their interface. I develop machine-learning methods for the numerical solution of PDEs and, conversely, use mathematical analysis to study machine learning and obtain a deeper theoretical understanding. My work covers new methodologies, rigorous convergence analysis, and practical engineering applications.

• AI for Science: Scientific machine learning with rigorous convergence analysis

• Mathematics of Deep Learning: Mathematical theory of neural networks 

• Numerical analysis of Nonlinear PDEs: Finite element methods with underlying PDE analysis

Publications & Preprints

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

Kyueon Choi, Kyungkeun Kang and Seungchan Ko, Mathematical Models and Methods in Applied Sciences (M3AS) (accepted for publication), (2025).

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

Youngjoon Hong, Seungchan Ko and Jae Yong Lee, IMA Journal of Numerical Analysis (accepted for publication), (2025).

• 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).

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

Youngjoon Hong, Jae Yong Lee and Seungchan Ko SIAM Journal on Scientific Computing,  Vol. 47, Iss. 2 (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,  Journal of Computational Physics, Volume 529, 113860  (2025).

• *Data-free Asymptotics-Informed Operator Networks for Singularly Perturbed PDEs

Jinsil Lee, Youngjoon Hong, Seungchan Ko, Jae Yong Lee, arXiv:2512.22006 [math.NA], preprint (2025). 

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

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

• *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], preprint (2025).

• 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], preprint (2025).

• *A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticity

Josef Dick, Seungchan Ko, Quoc Thong Le Gia, Kassem Mustapha and Sanghyeon Park, arXiv:2505.21994 [math.NA], preprint (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).

• *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], preprint (2023).

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

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

• *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).

• *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: Mathematical Modelling and Numerical Analysis (M2AN), Volume 52 509–541 (2018).

*Corresponding Author

Lecture Notes

• Mathematical Theory of Machine Learning

Youngjoon Hong and Seungchan Ko (2025).

Patents

• 위상학적 데이터 분석을 이용한 웨이퍼 디펙 패턴 분류 방법

고승찬, 특허 제 10-2855690 호 (2025).

Finite Element Operator Network (FEONet)

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

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