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

authored by

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

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.

Organisation(s)

Institute of Photonics

External Organisation(s)

Beijing Institute of Technology
King Saud University
Tongji University

Type

Article

Journal

Engineering with computers

Volume

38

Pages

5423-5444

No. of pages

22

ISSN

0177-0667

Publication date

12.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Software, Engineering(all), Computer Science Applications, Modelling and Simulation

Electronic version(s)

https://doi.org/10.1007/s00366-022-01633-6 (Access: Open)