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.

翻译：我们提出了一种基于深度学习的数值模拟方法，用于求解双层板的大弯曲变形问题。受贪心算法启发，我们在嵌套域序列上构建了预训练策略，该方法能有效加速训练收敛过程，并更高效地定位全局极小值。所提方法展现出收敛至全局极小值的能力，克服了梯度流方法易陷入局部极小值区域的局限性。通过多组数值实验验证，本方法在极小值的相对能量误差和相对$L^2$误差方面均取得了更优表现。此外，我们的方法成功保持了等距约束的$L^2$范数，从而有效提升了数值解精度。