수학과

일시

2024.06.12.(수) 12:00 ~ 13:00

장소

팔달관 621호

발표자

정경진(데이터사이언스전공/석사과정)

Title

Deep Learning based PDE Solver

Abstract

Partial differential equations (PDEs) are crucial in modeling various physical phenomena. In this study, we introduce a novel deep learning approach to solve the Poisson equation using convolutional autoencoders. Our method leverages a dataset of function pairs representing source terms and boundary conditions to train the autoencoder model. Once trained, the model can efficiently and rapidly approximate solutions to the Poisson equation for new source terms and boundary conditions without additional training. This approach eliminates the reliance on traditional numerical methods such as the Finite Element Method (FEM), offering significant advantages in terms of inference speed and flexibility. Our results highlight the potential of neural networks to provide accurate solutions for PDEs with non-homogeneous boundary conditions and varying source terms, demonstrating the effectiveness of data-driven models in solving complex physical problems.