Finite Difference Nets: A Deep Recurrent Framework for Solving Evolution PDEs
Numerical Analysis
2021-04-21 v1 Numerical Analysis
Abstract
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data sets. We provide a new perspective, that is, a different type of architecture through exploring the possible connections between traditional numerical methods (such as finite difference schemes) and deep neural networks, particularly convolutional and fully-connected neural networks. Our proposed approach will show its effectiveness and efficiency in solving PDE models with an integral form, in particular, we test on one-way wave equations and system of conservation laws.
Cite
@article{arxiv.2104.09625,
title = {Finite Difference Nets: A Deep Recurrent Framework for Solving Evolution PDEs},
author = {Cheng Chang and Liu Liu and Tieyong Zeng},
journal= {arXiv preprint arXiv:2104.09625},
year = {2021}
}