3 papers
math.NA2021
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…
math.NA2021
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…
math.NA2019
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…