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 - <p style="text-align: justify;">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.</p>