3 citations · 4 across the 6 of their papers we have counts for
6 papers
Robust training and rigorous error analysis of physics-informed neural networks for the -Laplace equation
Kyueon Choi, Seungchan Ko, Dohyun Kwon
With the rise of scientific machine learning, physics-informed neural networks (PINNs) have been extensively applied to a wide range of problems. Nevertheless, most theoretical ana…
Sobolev Approximation of Deep ReLU Networks in Log-Barron Space
Changhoon Song, Seungchan Ko, Youngjoon Hong
Universal approximation theorems show that neural networks can approximate any continuous function; however, the number of parameters may grow exponentially with the ambient dimens…
Data-Free Asymptotics-Informed Operator Networks for Singularly Perturbed PDEs
Jinsil Lee, Youngjoon Hong, Seungchan Ko +1
Recent advances in machine learning (ML) have opened new possibilities for solving partial differential equations (PDEs), yet robust performance in challenging regimes remains limi…
Sparse FEONet: A Low-Cost, Memory-Efficient Operator Network via Finite-Element Local Sparsity for Parametric PDEs
Seungchan Ko, Jiyeon Kim, Dongwook Shin
In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, F…
Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs
Youngjoon Hong, Seungchan Ko, Jaeyong Lee
In this paper, we provide a theoretical analysis of a type of operator learning method without data reliance based on the classical finite element approximation, which is called th…
Finite Element Operator Network for Solving Elliptic-type parametric PDEs
Jae Yong Lee, Seungchan Ko, Youngjoon Hong
Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, s…