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math.NA2024★ 2 cited
Stochastic approach for elliptic problems in perforated domains
Jihun Han, Yoonsang Lee
A wide range of applications in science and engineering involve a PDE model in a domain with perforations, such as perforated metals or air filters. Solving such perforated domain…
math.NA2023
An analysis of the derivative-free loss method for solving PDEs
Jihun Han, Yoonsang Lee
This study analyzes the derivative-free loss method to solve a certain class of elliptic PDEs and fluid problems using neural networks. The approach leverages the Feynman-Kac formu…