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

Hongwei Guo, Xiaoying Zhuang, Pengwan Chen, Naif Alajlan, Timon Rabczuk*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)

Abstract

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 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.

Original languageEnglish
Pages (from-to)5423-5444
Number of pages22
JournalEngineering with Computers
Volume38
Issue number6
DOIs
Publication statusPublished - Dec 2022

Keywords

  • Activation function
  • Collocation method
  • Deep learning
  • Non-homogeneous
  • PDEs
  • Physics-informed
  • Potential problem
  • Sampling method
  • Sensitivity analysis
  • Transfer learning

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