5 papers
Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations
Chanyoung Kim, Myeonghwan Seong, Yujin Kim +2
Partial differential equations (PDEs) are central to modeling physical and engineering systems, but repeatedly solving parametric PDEs remains computationally expensive. Operator l…
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…
Discontinuous Galerkin finite element operator network for solving non-smooth PDEs
Kapil Chawla, Youngjoon Hong, Jae Yong Lee +1
We introduce Discontinuous Galerkin Finite Element Operator Network (DG--FEONet), a data-free operator learning framework that combines the strengths of the discontinuous Galerkin…
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…