Analysis of three-dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis

  • In this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network includingIn this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilized for non-homogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations.show moreshow less

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Metadaten
Document Type:Article
Author: Hongwei Guo, Xiaoying Zhuang, Pengwan Chen, Naif AlajlanORCiD, Prof. Dr.-Ing. Timon RabczukORCiDGND
DOI (Cite-Link):https://doi.org/10.1007/s00366-022-01633-6Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20220811-46764Cite-Link
URL:https://link.springer.com/article/10.1007/s00366-022-01633-6
Parent Title (English):Engineering with Computers
Language:English
Date of Publication (online):2022/07/22
Date of first Publication:2022/03/25
Release Date:2022/08/11
Publishing Institution:Bauhaus-Universität Weimar
Institutes and partner institutions:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
Volume:2022
Pagenumber:22
First Page:1
Last Page:22
Tag:Activation function; Collocation method; Potential problem; Transfer learning
GND Keyword:Deep learning; Kollokationsmethode
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)