13 citations · 30 across the 8 of their papers we have counts for
4 papers · 1 filter
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…