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arXiv · 2104.09625

Finite Difference Nets: A Deep Recurrent Framework for Solving Evolution PDEs

Cheng Chang·Liu Liu·Tieyong Zeng
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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.

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Cheng Chang, Liu Liu, Tieyong Zeng. 2021-04-16. Finite Difference Nets: A Deep Recurrent Framework for Solving Evolution PDEs. https://arxiv.org/abs/2104.09625

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