40 citations · 85 across the 20 of their papers we have counts for
11 papers · 1 filter
Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems
Marc Haltmayer, Jaemin Seo, Yuseung Lee +3
Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretiz…
A residual-based finite element surrogate solver for elliptic partial differential equations
Kyoungjin Jung, Jae Yong Lee, Dongwook Shin
We propose a residual-based finite element surrogate solver for elliptic partial differential equations. The method combines convolutional neural networks with classical finite ele…
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…
Deep learning-based moment closure for multi-phase computation of semiclassical limit of the Schrödinger equation
Jin Woo Jang, Jae Yong Lee, Liu Liu +1
We present a deep learning approach for computing multi-phase solutions to the semiclassical limit of the Schrödinger equation. Traditional methods require deriving a multi-phase a…
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…
Structure-Preserving Operator Learning: Modeling the Collision Operator of Kinetic Equations
Jae Yong Lee, Steffen Schotthöfer, Tianbai Xiao +2
This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a…
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…
opPINN: Physics-Informed Neural Network with operator learning to approximate solutions to the Fokker-Planck-Landau equation
Jae Yong Lee, Juhi Jang, Hyung Ju Hwang
We propose a hybrid framework opPINN: physics-informed neural network (PINN) with operator learning for approximating the solution to the Fokker-Planck-Landau (FPL) equation. The o…
The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach
Jae Yong Lee, Jin Woo Jang, Hyung Ju Hwang
The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time. In…
Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach
Hyung Ju Hwang, Jin Woo Jang, Hyeontae Jo +1
The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximate…