Year: 2024
Author: Xiang Li, Yulei Liao, Pingbing Ming
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-325.070124
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 3 : pp. 551–578
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Deep learning pre-training method nonlinear elasticity bilayer bending isometric constraint.