40 citations · 85 across the 20 of their papers we have counts for
20 papers
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…
Unbiased and Second-Order-Free Training for High-Dimensional PDEs
Jaemin Seo, Surin Lee, Jae Yong Lee
Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving h…
Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation
Sum Kyun Song, Bong Gyun Shin, Jae Yong Lee
Discovering governing differential equations from observational data is a fundamental challenge in scientific machine learning. Existing symbolic regression approaches rely primari…
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…
FourierSpecNet: Neural Collision Operator Approximation Inspired by the Fourier Spectral Method for Solving the Boltzmann Equation
Jae Yong Lee, Gwang Jae Jung, Byung Chan Lim +1
The Boltzmann equation, a fundamental model in kinetic theory, describes the evolution of particle distribution functions through a nonlinear, high-dimensional collision operator.…
Conformal mapping based Physics-informed neural networks for designing neutral inclusions
Daehee Cho, Hyeonmin Yun, Jaeyong Lee +1
We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Infor…
Hamilton-Jacobi Based Policy-Iteration via Deep Operator Learning
Jae Yong Lee, Yeoneung Kim
The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we i…
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…
Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids
Sung Woong Cho, Jae Yong Lee, Hyung Ju Hwang
Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of…
HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork
Jae Yong Lee, Sung Woong Cho, Hyung Ju Hwang
Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even m…
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…
Pseudo-Differential Neural Operator: Generalized Fourier Neural Operator for Learning Solution Operators of Partial Differential Equations
Jin Young Shin, Jae Yong Lee, Hyung Ju Hwang
Learning the mapping between two function spaces has garnered considerable research attention. However, learning the solution operator of partial differential equations (PDEs) rema…
Solving PDE-constrained Control Problems Using Operator Learning
Rakhoon Hwang, Jae Yong Lee, Jin Young Shin +1
The modeling and control of complex physical systems are essential in real-world problems. We propose a novel framework that is generally applicable to solving PDE-constrained opti…
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…