[P] In preparation

[P6] FourierSpecNet: Neural Collision Operator Approximation Inspired by the Fourier Spectral Method for Solving the Boltzmann Equation

Jae Yong Lee, Gwang Jae Jung*, Byungchan Lim*, Hyung Ju Hwang

Under review. arXiv:2504.20408 [math.NA]

[P5] Deep learning-based moment closure for multi-phase computation of semiclassical limit of the Schrödinger equation

Jin Woo Jang*, Jae Yong Lee*, Liu Liu*, Zhenyi Zhu*

Under review. arXiv:2504.08341 [math.NA]

[P4] Conformal mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs): learning neural networks for designing neutral inclusions

Daehee Cho, Hyeonmin Yun, Jaeyong Lee, Mikyoung Lim

Preprint. arXiv:2501.07809 [cs.LG]

[P3] Hamilton-Jacobi Based Policy-Iteration via Deep Operator Learning

Jae Yong Lee, Yeoneung Kim

Under review. arXiv:2406.10920 [math.OC]

[P2] Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs

Youngjoon Hong*, Seungchan Ko*, Jae Yong Lee*

Under review. arXiv:2404.17868 [math.NA]

[P1] Structure-Preserving Operator Learning: Modeling the Collision Operator of Kinetic Equations

Jae Yong Lee*, Steffen Schotthöfer*, Tianbai Xiao*, Sebastian Krumscheid, Martin Frank

Preprint. arXiv:2402.16613 [math.NA]

[C4] Isometric Regularization for Manifolds of Functional Data (Project page)

Hyeongjun Heo, Seonghun Oh, Jae Yong Lee, Young Min Kim, Yonghyeon Lee

International Conference on Learning Representation (ICLR), 2025.

[J5] Finite Element Operator Network for Solving Elliptic-type parametric PDEs (Project page)

Jae Yong Lee, Seungchan Ko*, Youngjoon Hong*

SIAM Journal on Scientific Computing (SISC), 2025.

[C3] Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids

SungWoong Cho*, Jae Yong Lee*, Hyung Ju Hwang

ICLR 2024 Workshop on AI4DifferentialEquations In Science, 2024

[J4] Pseudo-Differential Neural Operator: Generalize Fourier Neural operator for Learning Solution Operators of Partial Differential Equations

Jin Young Shin*, Jae Yong Lee*, Hyung Ju Hwang

Transactions on Machine Learning Research (TMLR), 2024,

[D1] 물리 정보 기계학습 의 발전 및 응용

Jae Yong Lee* and Hwijae Son*

전자공학회지 제50권 6호, 2023

[J3] 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

Journal of Computational Physics (JCP), 2023.

[C2] HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork

Jae Yong Lee*, SungWoong Cho*, Hyung Ju Hwang

International Conference on Learning Representation (ICLR), 2023.

[C1] Solving PDE-constrained Control Problems using Operator Learning

Rakhoon Hwang*, Jae Yong Lee*, Jin Young Shin*, Hyung Ju Hwang

Association for the Advancement of Artificial Intelligence (AAAI), 2022.

[J2] 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, and Hyung Ju Hwang

ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2021.

[J1] Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach

Hyung Ju Hwang*, Jin Woo Jang*, Hyeontae Jo*, and Jae Yong Lee*

Journal of Computational Physics (JCP), 2020.

On the Neural Network approach to the Vlasov-Poisson-Fokker-Planck system and its diffusion limit

KSIAM Newsletter(2024. 5, Vol.8 , No.1) "연산자 학습을 이용한 실시간 편미분방정식 시뮬레이션"

• Hyung Ju Hwang (POSTECH, South Korea)

• Jin Woo Jang (POSTECH, South Korea)

• Hyeontae Jo (Korea University, South Korea)

• Rakhoon Hwang (Hyundai Motor Company, South Korea)

• Jin Young Shin (Samsung Advanced Institute of Technology, South Korea)

• SungWoong Cho (SAARC, South Korea)

• Juhi Jang (University of Southern California, USA)

• Hwijae Son (Konkuk University, South Korea)

• Seungchan Ko (Inha University, South Korea)

• Youngjoon Hong (Seoul National University, South Korea)

• Young Min Kim (Seoul National University, South Korea)

• Yonghyeon Lee (Massachusetts Institute of Technology(MIT), USA)

• Steffen Schotthöfer (Oak Ridge National Laboratory, USA)

• Tianbai Xiao (University of Chinese Academy of Sciences, China)

• Sebastian Krumscheid (Karlsruhe Institute of Technology, German)

• Martin Frank (Karlsruhe Institute of Technology, German)

• Yeoneung Kim (Seoul National University of Science and Technology, South Korea)

• Mikyoung Lim (KAIST, South Korea)

• Daehee Cho (KAIST, South Korea)

• Gwang Jae Jung (POSTECH, South Korea)

• Liu Liu (CUHK, Hong Kong)

• Yeonjong Shin (NC State University, USA)