FEA-net: A deep convolutional neural network with physics prior for efficient data driven pde learning

Houpu Yao, Yi Ren, Yongming Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We present FEA-Net as an efficient data driven approach to learn Partial Differential Equation (PDE). Specially designed based on physics prior knowledge, FEA-Net needs less trainable parameters and training data while has certifiable convergence. Moreover, FEA-Net is fully interpretable and we can even infer the physics parameters from it. In this paper, inspired by the local support of Finite Element Analysis (FEA), we will first construct a convolution kernel that is suitable to model PDE. Secondly, inspired by the numerical solvers, we constructed the FEA-Net based on the proposed convolution kernel. Experiment results in predicting elasticity problems show that, FEA-Net is able to outperform purely data driven approaches like Fully Convolutional Networks (FCN) by a large margin on multiple tasks.

Original languageEnglish (US)
Title of host publicationAIAA Scitech 2019 Forum
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624105784
DOIs
StatePublished - Jan 1 2019
EventAIAA Scitech Forum, 2019 - San Diego, United States
Duration: Jan 7 2019Jan 11 2019

Publication series

NameAIAA Scitech 2019 Forum

Conference

ConferenceAIAA Scitech Forum, 2019
CountryUnited States
CitySan Diego
Period1/7/191/11/19

ASJC Scopus subject areas

  • Aerospace Engineering

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