A pre-training deep learning method for simulating the large bending deformation of bilayer plates

TL;DR

This paper introduces a deep learning pre-training approach inspired by greedy algorithms to efficiently simulate large bending deformations of bilayer plates, overcoming local minima issues and improving accuracy.

Contribution

A novel pre-training deep learning method for bilayer plate deformation simulation that accelerates convergence and maintains isometric constraints.

Findings

Faster convergence to the absolute minimizer.

Better accuracy with fewer degrees of freedom.

Successfully maintains isometric constraints.

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.