Abstract

The problem of generating microstructures of complex materials in silico has been approached from various directions including simulation, Markov, deep learning and descriptor-based approaches. This work presents a hybrid method that is inspired by all four categories and has interesting scalability properties. A neural cellular automaton is trained to evolve microstructures based on local information. Unlike most machine learning-based approaches, it does not directly require a data set of reference micrographs, but is trained from statistical microstructure descriptors that can stem from a single reference. This means that the training cost scales only with the complexity of the structure and associated descriptors. Since the size of the reconstructed structures can be set during inference, even extremely large structures can be efficiently generated. Similarly, the method is very efficient if many structures are to be reconstructed from the same descriptor for statistical evaluations. The method is formulated and discussed in detail by means of various numerical experiments, demonstrating its utility and scalability.

中文翻译：

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使用神经元胞自动机从统计描述符重建微观结构

摘要

在计算机中生成复杂材料的微观结构的问题已经从各个方向得到解决，包括模拟、马尔可夫、深度学习和基于描述符的方法。这项工作提出了一种混合方法，该方法受到所有四个类别的启发，并且具有有趣的可扩展性特性。神经元胞自动机经过训练，可以根据局部信息演化微结构。与大多数基于机器学习的方法不同，它并不直接需要参考显微照片的数据集，而是根据来自单个参考的统计微观结构描述符进行训练。这意味着训练成本仅随着结构和相关描述符的复杂性而变化。由于可以在推理过程中设置重建结构的大小，因此即使非常大的结构也可以有效地生成。类似地，如果要从相同的描述符重建许多结构以进行统计评估，则该方法非常有效。通过各种数值实验对该方法进行了详细的阐述和讨论，证明了其实用性和可扩展性。