使用卷积编码器-解码器学习预测微结构材料中的峰值应力
Predicting Peak Stresses In Microstructured Materials Using Convolutional Encoder-Decoder Learning
AI总结：
本文提出卷积编码器-解码器深度学习方法，从合成微结构预测线弹性应力场并检测峰值应力簇，实验表明其能准确捕捉簇的几何特征。
摘要：
本工作提出了一种机器学习方法，用于预测非均质多晶材料中的峰值应力簇。以往在力学背景下使用机器学习的工作主要集中于预测应力场的有效响应和整体结构。然而，它们预测峰值应力的能力尚未得到探索，而峰值应力对于失效至关重要；这是因为峰值应力簇相对于整个计算域只占据很小的空间体积，因此需要计算成本高昂的训练。本工作开发了一种基于深度学习的卷积编码器-解码器方法，专注于预测峰值应力簇，特别是在非均质线弹性框架下预测这些簇的尺寸和其他特征。该方法基于卷积滤波器，通过空间加权平均操作来建模微结构与应力场之间的局部空间关系。模型首先在合成生成的微结构中，针对所施加宏观应变下应力的线弹性计算结果进行训练，这些计算结果充当真值。随后，将训练后的模型用于在给定（合成生成的）微结构时预测应力场，进而检测所预测应力场内的峰值应力簇。通过使用余弦相似度指标，并将峰值应力簇的几何特征与真值计算结果进行比较，分析了峰值应力预测的准确性。观察结果表明，该模型能够学习并预测峰值应力簇的几何细节；尤其与较低的峰值应力值相比，模型在较高的（归一化）峰值应力值上表现更好。这些比较表明，所提出的方法非常适合预测峰值应力簇的特征。
英文摘要：
This work presents a machine learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective response and overall structure of stress fields. However, their ability to predict peak stresses -- which are of critical importance to failure -- is unexplored, because the peak-stress clusters occupy a small spatial volume relative to the entire domain, and hence requires computationally expensive training. This work develops a deep-learning based Convolutional Encoder-Decoder method that focuses on predicting peak-stress clusters, specifically on the size and other characteristics of the clusters in the framework of heterogeneous linear elasticity. This method is based on convolutional filters that model local spatial relations between microstructures and stress fields using spatially weighted averaging operations. The model is first trained against linear elastic calculations of stress under applied macroscopic strain in synthetically-generated microstructures, which serves as the ground truth. The trained model is then applied to predict the stress field given a (synthetically-generated) microstructure and then to detect peak-stress clusters within the predicted stress field. The accuracy of the peak-stress predictions is analyzed using the cosine similarity metric and by comparing the geometric characteristics of the peak-stress clusters against the ground-truth calculations. It is observed that the model is able to learn and predict the geometric details of the peak-stress clusters and, in particular, performed better for higher (normalized) values of the peak stress as compared to lower values of the peak stress. These comparisons showed that the proposed method is well-suited to predict the characteristics of peak-stress clusters.
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