13 citations · 30 across the 8 of their papers we have counts for
9 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…
ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines
Hwijae Son
Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training D…
Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems
Sung Woong Cho, Hwijae Son
Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator l…
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…
The Deep Minimizing Movement Scheme
Min Sue Park, Cheolhyeong Kim, Hwijae Son +1
Solutions of certain partial differential equations (PDEs) are often represented by the steepest descent curves of corresponding functionals. Minimizing movement scheme was develop…
Lagrangian dual framework for conservative neural network solutions of kinetic equations
Hyung Ju Hwang, Hwijae Son
In this paper, we propose a novel conservative formulation for solving kinetic equations via neural networks. More precisely, we formulate the learning problem as a constrained opt…
Sobolev Training for Physics Informed Neural Networks
Hwijae Son, Jin Woo Jang, Woo Jin Han +1
Physics Informed Neural Networks (PINNs) is a promising application of deep learning. The smooth architecture of a fully connected neural network is appropriate for finding the sol…
Traveling Wave Solutions of Partial Differential Equations via Neural Networks
Sung Woong Cho, Hyung Ju Hwang, Hwijae Son
This paper focuses on how to approximate traveling wave solutions for various kinds of partial differential equations via artificial neural networks. A traveling wave solution is h…
Deep Neural Network Approach to Forward-Inverse Problems
Hyeontae Jo, Hwijae Son, Hyung Ju Hwang +1
In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the pr…