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Volume 14, Issue 3
A Pre-Training Deep Learning Method for Simulating the Large Bending Deformation of Bilayer Plates

Xiang Li, Yulei Liao & Pingbing Ming

East Asian J. Appl. Math., 14 (2024), pp. 551-578.

Published online: 2024-05

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  • Abstract

We propose a deep learning based method for simulating the large bending deformation of bilayer plates. Inspired by the greedy algorithm, we propose a pre-training method on a series of nested domains, which accelerate the convergence of training and find the absolute minimizer more effectively. The proposed method exhibits the capability to converge to an absolute minimizer, overcoming the limitation of gradient flow methods getting trapped in the local minimizer basins. We showcase better performance with fewer numbers of degrees of freedom for the relative energy errors and relative $L^2$-errors of the minimizer through numerical experiments. Furthermore, our method successfully maintains the $L^2$-norm of the isometric constraint, leading to an improvement of accuracy.

  • AMS Subject Headings

39-08, 49S05, 65Q20, 68T07, 74-10, 74G65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-14-551, author = {Li , XiangLiao , Yulei and Ming , Pingbing}, title = {A Pre-Training Deep Learning Method for Simulating the Large Bending Deformation of Bilayer Plates}, journal = {East Asian Journal on Applied Mathematics}, year = {2024}, volume = {14}, number = {3}, pages = {551--578}, abstract = {

We propose a deep learning based method for simulating the large bending deformation of bilayer plates. Inspired by the greedy algorithm, we propose a pre-training method on a series of nested domains, which accelerate the convergence of training and find the absolute minimizer more effectively. The proposed method exhibits the capability to converge to an absolute minimizer, overcoming the limitation of gradient flow methods getting trapped in the local minimizer basins. We showcase better performance with fewer numbers of degrees of freedom for the relative energy errors and relative $L^2$-errors of the minimizer through numerical experiments. Furthermore, our method successfully maintains the $L^2$-norm of the isometric constraint, leading to an improvement of accuracy.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-325.070124}, url = {http://global-sci.org/intro/article_detail/eajam/23161.html} }
TY - JOUR T1 - A Pre-Training Deep Learning Method for Simulating the Large Bending Deformation of Bilayer Plates AU - Li , Xiang AU - Liao , Yulei AU - Ming , Pingbing JO - East Asian Journal on Applied Mathematics VL - 3 SP - 551 EP - 578 PY - 2024 DA - 2024/05 SN - 14 DO - http://doi.org/10.4208/eajam.2023-325.070124 UR - https://global-sci.org/intro/article_detail/eajam/23161.html KW - Deep learning, pre-training method, nonlinear elasticity, bilayer bending, isometric constraint. AB -

We propose a deep learning based method for simulating the large bending deformation of bilayer plates. Inspired by the greedy algorithm, we propose a pre-training method on a series of nested domains, which accelerate the convergence of training and find the absolute minimizer more effectively. The proposed method exhibits the capability to converge to an absolute minimizer, overcoming the limitation of gradient flow methods getting trapped in the local minimizer basins. We showcase better performance with fewer numbers of degrees of freedom for the relative energy errors and relative $L^2$-errors of the minimizer through numerical experiments. Furthermore, our method successfully maintains the $L^2$-norm of the isometric constraint, leading to an improvement of accuracy.

Li , XiangLiao , Yulei and Ming , Pingbing. (2024). A Pre-Training Deep Learning Method for Simulating the Large Bending Deformation of Bilayer Plates. East Asian Journal on Applied Mathematics. 14 (3). 551-578. doi:10.4208/eajam.2023-325.070124
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