40 citations · 246 across the 34 of their papers we have counts for
37 papers
A Neural JKO Scheme for Hellinger-Kantorovich Gradient Flows via Monge-Growth Pairs
Geuntaek Seo, Cheolhyeong Kim, Hwijae Son +1
We develop a mesh-free neural JKO scheme for advection-reaction-diffusion equations with a gradient-flow structure in the Hellinger-Kantorovich (HK) geometry of unbalanced optimal…
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…
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…
Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)
Hwijae Son, Sung Woong Cho, Hyung Ju Hwang
Physics-Informed Neural Networks (PINNs) have become a prominent application of deep learning in scientific computation, as they are powerful approximators of solutions to nonlinea…
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…