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

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

Fingerprint

Physics
Neural networks
Finite element method
Convolution
Partial differential equations
Elasticity
Experiments

ASJC Scopus subject areas

  • Aerospace Engineering

Cite this

Yao, H., Ren, Y., & Liu, Y. (2019). FEA-net: A deep convolutional neural network with physics prior for efficient data driven pde learning. In AIAA Scitech 2019 Forum (AIAA Scitech 2019 Forum). American Institute of Aeronautics and Astronautics Inc, AIAA. https://doi.org/10.2514/6.2019-0680

FEA-net : A deep convolutional neural network with physics prior for efficient data driven pde learning. / Yao, Houpu; Ren, Yi; Liu, Yongming.

AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics Inc, AIAA, 2019. (AIAA Scitech 2019 Forum).

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

Yao, H, Ren, Y & Liu, Y 2019, FEA-net: A deep convolutional neural network with physics prior for efficient data driven pde learning. in AIAA Scitech 2019 Forum. AIAA Scitech 2019 Forum, American Institute of Aeronautics and Astronautics Inc, AIAA, AIAA Scitech Forum, 2019, San Diego, United States, 1/7/19. https://doi.org/10.2514/6.2019-0680
Yao H, Ren Y, Liu Y. FEA-net: A deep convolutional neural network with physics prior for efficient data driven pde learning. In AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics Inc, AIAA. 2019. (AIAA Scitech 2019 Forum). https://doi.org/10.2514/6.2019-0680
Yao, Houpu ; Ren, Yi ; Liu, Yongming. / FEA-net : A deep convolutional neural network with physics prior for efficient data driven pde learning. AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics Inc, AIAA, 2019. (AIAA Scitech 2019 Forum).
@inproceedings{dc3dd007ed854ca1b18653869a9d1f5f,
title = "FEA-net: A deep convolutional neural network with physics prior for efficient data driven pde learning",
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.",
author = "Houpu Yao and Yi Ren and Yongming Liu",
year = "2019",
month = "1",
day = "1",
doi = "10.2514/6.2019-0680",
language = "English (US)",
isbn = "9781624105784",
series = "AIAA Scitech 2019 Forum",
publisher = "American Institute of Aeronautics and Astronautics Inc, AIAA",
booktitle = "AIAA Scitech 2019 Forum",

}

TY - GEN

T1 - FEA-net

T2 - A deep convolutional neural network with physics prior for efficient data driven pde learning

AU - Yao, Houpu

AU - Ren, Yi

AU - Liu, Yongming

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85068971413&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068971413&partnerID=8YFLogxK

U2 - 10.2514/6.2019-0680

DO - 10.2514/6.2019-0680

M3 - Conference contribution

AN - SCOPUS:85068971413

SN - 9781624105784

T3 - AIAA Scitech 2019 Forum

BT - AIAA Scitech 2019 Forum

PB - American Institute of Aeronautics and Astronautics Inc, AIAA

ER -