定量分析评估应变薄膜表面弹性能的卷积神经网络预测性能
Quantitative analysis of the prediction performance of a Convolutional Neural Network evaluating the surface elastic energy of a strained film
AI总结：
本研究提出一种深度学习方法，利用Perlin噪声生成约19万个表面轮廓数据集训练全卷积神经网络，以预测起伏应力薄膜表面的弹性能密度，并验证了模型的定量预测精度、泛化能力及在表面演化问题中的鲁棒性。
摘要：
设计了一种深度学习方法来估计起伏应力薄膜自由表面的弹性能密度$ρ$。通过Perlin噪声随机生成了约190000个任意表面轮廓h(x)，并与相应的弹性能密度轮廓$ρ(x)$配对，这些$ρ(x)$通过适用于小斜率形态的半解析Green函数近似计算得出。由此产生的数据集及其较小的子集被用于训练全卷积神经网络。训练后的模型被证明能够返回$ρ$的定量预测，不仅体现在训练过程中损失函数的收敛，还体现在验证和测试中，且在较大的数据集情况下结果更好。进行了广泛的测试，以评估神经网络模型在应用于具有局部特征或原始数据集中未包含的指定几何形状的轮廓时的泛化能力。此外，还深入分析了其在超出训练所用域尺寸上的可能应用。突出了提供由Green近似计算的真实$ρ(x)$轮廓一对一再现的条件以及关键案例。深度学习得到的$ρ(x)$的准确性和鲁棒性在由蒸发/冷凝和表面扩散的简单偏微分方程描述的表面演化问题的时间积分中得到了进一步证明。
英文摘要：
A Deep Learning approach is devised to estimate the elastic energy density $ρ$ at the free surface of an undulated stressed film. About 190000 arbitrary surface profiles h(x) are randomly generated by Perlin noise and paired with the corresponding elastic energy density profiles $ρ(x)$, computed by a semi-analytical Green's function approximation, suitable for small-slope morphologies. The resulting dataset and smaller subsets of it are used for the training of a Fully Convolutional Neural Network. The trained models are shown to return quantitative predictions of $ρ$, not only in terms of convergence of the loss function during training, but also in validation and testing, with better results in the case of the larger dataset. Extensive tests are performed to assess the generalization capability of the Neural Network model when applied to profiles with localized features or assigned geometries not included in the original dataset. Moreover, its possible exploitation on domain sizes beyond the one used in the training is also analyzed in-depth. The conditions providing a one-to-one reproduction of the ground-truth $ρ(x)$ profiles computed by the Green's approximation are highlighted along with critical cases. The accuracy and robustness of the deep-learned $ρ(x)$ are further demonstrated in the time-integration of surface evolution problems described by simple partial differential equations of evaporation/condensation and surface diffusion.
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