Year: 2025
Author: Dan Li, Xinming Lu, Hongjuan Wang, Guibin Liu, Xin Liu
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 4 : pp. 1239–1258
Abstract
In this paper, we utilize Physics-Informed Neural Networks (PINNs) without any labeled data to solve the fourth-order partial differential equation governing the bending of thin plates. We meticulously formulate and apply our framework to the bending problem of elastic thin plates. Our findings indicate that defining each solution variable through an independent network, meaning without shared network parameters, yields superior performance compared to a single-network model with multiple outputs. During the training process, we discovered that more accurate results were achieved by adjusting the network architecture to strictly satisfy the boundary conditions, rather than incorporating them as part of the loss function. Remarkably, the PINNs are capable of obtaining relatively good results without the use of any labeled data during training, irrespective of whether soft or hard constraints are applied. In the end, the neural network’s predictions for plate deflection, stress, strain, bending, and shear force all have errors less than 5% compared to the analytical solutions. In the algorithm implementation phase, we leverage the Python library DeepXDE, which facilitates the training of PINNs by providing an efficient and expedited process.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0253
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 4 : pp. 1239–1258
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: PINNs elastic thin plates independent network without labeled data DeepXDE.