Details
| Original language | English |
|---|---|
| Pages (from-to) | 5423-5444 |
| Number of pages | 22 |
| Journal | Engineering with computers |
| Volume | 38 |
| Issue number | 6 |
| Early online date | 25 Mar 2022 |
| Publication status | Published - Dec 2022 |
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.
Keywords
- Activation function, Collocation method, Deep learning, Non-homogeneous, PDEs, Physics-informed, Potential problem, Sampling method, Sensitivity analysis, Transfer learning
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Engineering(all)
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Modelling and Simulation
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In: Engineering with computers, Vol. 38, No. 6, 12.2022, p. 5423-5444.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Analysis of three-dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis
AU - Guo, Hongwei
AU - Zhuang, Xiaoying
AU - Chen, Pengwan
AU - Alajlan, Naif
AU - Rabczuk, Timon
N1 - Funding information: The authors extend their appreciation to the Distinguished Scientist Fellowship Program (DSFP) at King Saud University for funding this work.
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - Activation function
KW - Collocation method
KW - Deep learning
KW - Non-homogeneous
KW - PDEs
KW - Physics-informed
KW - Potential problem
KW - Sampling method
KW - Sensitivity analysis
KW - Transfer learning
UR - http://www.scopus.com/inward/record.url?scp=85127206257&partnerID=8YFLogxK
U2 - 10.1007/s00366-022-01633-6
DO - 10.1007/s00366-022-01633-6
M3 - Article
VL - 38
SP - 5423
EP - 5444
JO - Engineering with computers
JF - Engineering with computers
SN - 0177-0667
IS - 6
ER -