Mathematics (May 2023)
Transfer Learning-Based Coupling of Smoothed Finite Element Method and Physics-Informed Neural Network for Solving Elastoplastic Inverse Problems
Abstract
In practical engineering applications, there is a high demand for inverting parameters for various materials, and obtaining monitoring data can be costly. Traditional inverse methods often involve tedious computational processes, require significant computational effort, and exhibit slow convergence speeds. The recently proposed Physics-Informed Neural Network (PINN) has shown great potential in solving inverse problems. Therefore, in this paper, we propose a transfer learning-based coupling of the Smoothed Finite Element Method (S-FEM) and PINN methods for the inversion of parameters in elastic-plasticity problems. The aim is to improve the accuracy and efficiency of parameter inversion for different elastic-plastic materials with limited data. High-quality small datasets were synthesized using S-FEM and subsequently combined with PINN for pre-training purposes. The parameters of the pre-trained model were saved and used as the initial state for the PINN model in the inversion of new material parameters. The inversion performance of the coupling of S-FEM and PINN is compared with the coupling of the conventional Finite Element Method (FEM) and PINN on a small data set. Additionally, we compared the efficiency and accuracy of both the transfer learning-based and non-transfer learning-based methods of the coupling of S-FEM and PINN in the inversion of different material parameters. The results show that: (1) our method performs well on small datasets, with an inversion error of essentially less than 2%; (2) our approach outperforms the coupling of conventional FEM and PINN in terms of both computational accuracy and computational efficiency; and (3) our approach is at least twice as efficient as the coupling of S-FEM and PINN without transfer learning, while still maintaining accuracy. Our method is well-suited for the inversion of different material parameters using only small datasets. The use of transfer learning greatly improves computational efficiency, making our method an efficient and accurate solution for reducing computational cost and complexity in practical engineering applications.
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