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Computational Mechanics

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28.11.2022 | Original Paper

A physics-informed neural network technique based on a modified loss function for computational 2D and 3D solid mechanics

verfasst von: Jinshuai Bai, Timon Rabczuk, Ashish Gupta, Laith Alzubaidi, Yuantong Gu

Erschienen in: Computational Mechanics | Ausgabe 3/2023

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Abstract

Despite its rapid development, Physics-Informed Neural Network (PINN)-based computational solid mechanics is still in its infancy. In PINN, the loss function plays a critical role that significantly influences the performance of the predictions. In this paper, by using the Least Squares Weighted Residual (LSWR) method, we proposed a modified loss function, namely the LSWR loss function, which is tailored to a dimensionless form with only one manually determined parameter. Based on the LSWR loss function, an advanced PINN technique is developed for computational 2D and 3D solid mechanics. The performance of the proposed PINN technique with the LSWR loss function is tested through 2D and 3D (geometrically nonlinear) problems. Thoroughly studies and comparisons are conducted between the two existing loss functions, the energy-based loss function and the collocation loss function, and the proposed LSWR loss function. Through numerical experiments, we show that the PINN based on the LSWR loss function is effective, robust, and accurate for predicting both the displacement and stress fields. The source codes for the numerical examples in this work are available at https://github.com/JinshuaiBai/LSWR_loss_function_PINN/.

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Titel: A physics-informed neural network technique based on a modified loss function for computational 2D and 3D solid mechanics
verfasst von: Jinshuai Bai
Timon Rabczuk
Ashish Gupta
Laith Alzubaidi
Yuantong Gu
Publikationsdatum: 28.11.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Computational Mechanics / Ausgabe 3/2023
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI: https://doi.org/10.1007/s00466-022-02252-0

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