基于差异的深度学习框架用于异构介质中的压力预测
Difference-Based Deep Learning Framework for Stress Predictions in Heterogeneous Media
摘要：
使用有限元分析（FEA）对非均匀介质（如复合材料）进行应力分析已成为设计和分析中的常见问题。然而，在优化和多尺度等情况下，使用FEA确定非均匀介质中的应力分布在计算上可能是昂贵的。为了解决这个问题，我们利用深度学习开发了一套基于工程和统计知识的新型差分神经网络（DiNN）框架，以首次确定非均匀介质中的应力分布，特别关注表现出高应力集中的不连续区域。我们的方法的新颖之处在于，我们不是像以前那样直接使用几个FEA模型几何形状和应力作为训练神经网络的输入，而是专注于突出不同输入样本之间应力分布的差异，以提高非均匀介质中预测的准确性。我们通过考虑复合材料分析中常用的不同类型的几何模型（包括体积分数和空间随机性）来评估DiNN框架的性能。结果表明，DiNN结构显着提高应力预测的准确性相比，现有的结构，特别是对于随机体积分数的复合材料模型时，局部高应力集中。
英文摘要：
Stress analysis of heterogeneous media, like composite materials, using Finite Element Analysis (FEA) has become commonplace in design and analysis. However, determining stress distributions in heterogeneous media using FEA can be computationally expensive in situations like optimization and multi-scaling. To address this, we utilize Deep Learning for developing a set of novel Difference-based Neural Network (DiNN) frameworks based on engineering and statistics knowledge to determine stress distribution in heterogeneous media, for the first time, with special focus on discontinuous domains that manifest high stress concentrations. The novelty of our approach is that instead of directly using several FEA model geometries and stresses as inputs for training a Neural Network, as typically done previously, we focus on highlighting the differences in stress distribution between different input samples for improving the accuracy of prediction in heterogeneous media. We evaluate the performance of DiNN frameworks by considering different types of geometric models that are commonly used in the analysis of composite materials, including volume fraction and spatial randomness. Results show that the DiNN structures significantly enhance the accuracy of stress prediction compared to existing structures, especially for composite models with random volume fraction when localized high stress concentrations are present.
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