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.…
Document Type: | Article |
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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 (ISM) |
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): | Creative Commons 4.0 - Namensnennung (CC BY 4.0) |