Deep learning of surface elastic chemical potential in strained films: from statics to dynamics

We develop a convolutional neural network (NN) approach able to predict the elastic contribution to chemical potential μₑ at the surface of a 2D strained film given its profile h(x). Arbitrary h(x) profiles are obtained by using a Perlin Noise generator and the corresponding μₑ profiles are calculated either by a Green's function approximation (GA) or by Finite Element Method (FEM). First, a large dataset is produced by exploiting the GA method and it is then used for the training of the NN model. The performance of the trained NN is extensively examined, demonstrating its ability to predict μₑ looking both to the training/validation set and to an additional testing set containing different profiles, including sinusoids, gaussians and sharp peaks never considered in the NN training. The NN is then applied to simulate the morphological evolution of strained Ge films, where the predicted μₑ at each integration timestep plays the role of driving force for material redistribution in competition with a surface energy term (proportional to local curvature) and eventually a wetting energy contribution. Both surface diffusion and evaporation/condensation dynamics are considered and the proposed NN approach is shown to well match the evolution expected by using GA. On this basis, a smaller dataset is built with μₑ profiles calculated by FEM and a new NN model is trained on it. Once again the trained NN-model returns reliable prediction of the FEM μₑ. The findings suggest that the proposed NN-based strategy can be used in replacement of the computationally intensive FEM calculations, enabling the simulation of larger scales and longer time scales untreatable by direct FEM calculation.

本研究开发了一种卷积神经网络（NN）方法，能够根据二维应力薄膜的轮廓h(x)预测其表面化学势μₑ的弹性贡献。通过使用Perlin噪声生成器获得任意h(x)轮廓，相应的μₑ轮廓则通过格林函数近似（GA）或有限元方法（FEM）进行计算。首先，通过GA方法生成大量数据集，随后用于训练NN模型。经过广泛的性能评估，该NN模型展现出预测μₑ的能力，无论是在训练/验证集上，还是在包含正弦波、高斯波和锐峰等不同轮廓的额外测试集上，均能给出可靠的预测结果。随后，NN模型被应用于模拟应力Ge薄膜的形态演化，其中在每个积分时间步长预测的μₑ充当驱动力，以促进材料重新分布，并与其表面能项（与局部曲率成正比）和最终湿润能贡献进行竞争。同时考虑了表面扩散和蒸发/凝结动力学，并显示出所提出的NN方法与使用GA预期的演化过程高度吻合。在此基础上，构建了一个较小的数据集，其中的μₑ轮廓通过FEM计算得到，并在其上训练了新的NN模型。同样，训练后的NN模型对FEM计算的μₑ进行了可靠的预测。研究结果表明，所提出的基于NN的策略可以替代计算密集型的FEM计算，从而实现更大规模和更长时间尺度的模拟，这些模拟直接FEM计算无法实现。