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

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 can 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 local minimizer basins. We showcase better performance for the relative energy errors and relative $L^2$-errors of the minimizer through several numerical experiments. Furthermore, our method successfully maintains the $L^2$-norm of the isometric constraint, leading to improved solution accuracy.