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.

翻译：我们提出了一种基于深度学习的方法，用于模拟双层板的大弯曲变形。受贪心算法启发，我们提出了一种在嵌套域序列上的预训练方法，该方法加速了训练的收敛，并更有效地找到了全局极小值点。所提出的方法展现出收敛到全局极小值的能力，克服了梯度流方法陷入局部极小值点的局限。通过数值实验，我们展示了该方法在相对能量误差和极小值点相对$L^2$误差方面，使用更少的自由度即可达到更优性能。此外，我们的方法成功保持了等距约束的$L^2$范数，从而提高了精度。