Abstract Heterogeneous materials, whether natural or artificial, are usually composed of distinct constituents present in complex microstructures with discontinuous, irregular and hierarchical characteristics. For many heterogeneous materials, such as porous media and composites, the microstructural features are of fundamental importance for their macroscopic properties. This paper presents a novel method to statistically characterize and reconstruct random microstructures through a deep neural network (DNN) model, which can be used to study the microstructure–property relationships. In our method, the digital microstructure image is assumed to be a stationary Markov random field (MRF), and local patterns covering the basic morphological features are collected to train a DNN model, after which statistically equivalent samples can be generated through a DNN-guided reconstruction procedure. Furthermore, to overcome the short-distance limitation associated with the MRF assumption, a multi-level approach is developed to preserve the long-distance morphological features of heterogeneous microstructures. A large number of tests have been conducted to compare the reconstructed and target microstructures in both morphological characteristics and physical properties, and good agreements are observed in all test cases. The proposed method is efficient, accurate, versatile, and especially beneficial to the statistical reconstruction of 2D/3D microstructures with long-distance correlations.

中文翻译：

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使用深度神经网络对异质微观结构进行统计表征和重建

摘要 非均质材料，无论是天然的还是人造的，通常由存在于复杂微观结构中的不同成分组成，具有不连续、不规则和分层特征。对于许多异质材料，例如多孔介质和复合材料，微观结构特征对其宏观特性至关重要。本文提出了一种通过深度神经网络 (DNN) 模型统计表征和重建随机微观结构的新方法，该方法可用于研究微观结构 - 性能关系。在我们的方法中，数字微结构图像被假定为平稳马尔可夫随机场（MRF），并收集覆盖基本形态特征的局部模式来训练 DNN 模型，之后，可以通过 DNN 引导的重建程序生成统计等效的样本。此外，为了克服与 MRF 假设相关的短距离限制，开发了一种多级方法来保留异质微结构的长距离形态特征。已经进行了大量测试来比较重建和目标微观结构的形态特征和物理性能，并且在所有测试案例中都观察到良好的一致性。该方法高效、准确、通用，特别有利于长距离相关的 2D/3D 微观结构的统计重建。开发了一种多层次的方法来保留异质微结构的长距离形态特征。已经进行了大量测试来比较重建和目标微观结构的形态特征和物理性能，并且在所有测试案例中都观察到良好的一致性。该方法高效、准确、通用，特别有利于长距离相关的 2D/3D 微观结构的统计重建。开发了一种多层次的方法来保留异质微结构的长距离形态特征。已经进行了大量测试来比较重建和目标微观结构的形态特征和物理性能，并且在所有测试案例中都观察到良好的一致性。该方法高效、准确、通用，特别有利于长距离相关的 2D/3D 微观结构的统计重建。