Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically evolving microstructures. The ability to rapidly compute the macroscopic behavior based on these detailed microstructures is of paramount importance for accelerating material discovery and design. Here, our focus is on the macroscopic, nonlinear elastic response of materials harboring microstructure. Because of the diversity of microstructural patterns that can form, there is interest in taking a purely computational approach to predicting their macroscopic response. However, the evaluation of macroscopic, nonlinear elastic properties purely based on direct numerical simulations (DNS) is computationally very expensive, and hence impractical for material design when a large number of microstructures need to be tested. A further complexity of a hierarchical nature arises if the elastic free energy and its variation with strain is a small-scale fluctuation on the dominant trajectory of the total free energy driven by microstructural dynamics. To address these challenges, we present a data-driven approach, which combines advanced neural network (NN) models with DNS to predict the homogenized, macroscopic, mechanical free energy and stress fields arising in a family of multi-component crystalline solids that develop microstructure. The hierarchical structure of the free energy's evolution induces a multi-resolution character to the machine learning paradigm: We construct knowledge-based neural networks (KBNNs) with either pre-trained fully connected deep neural networks (DNNs), or pre-trained convolutional neural networks (CNNs) that describe the dominant characteristic of the data to fully represent the hierarchically evolving free energy.

中文翻译：

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机器学习材料物理学：多分辨率神经网络学习进化微结构的自由能和非线性弹性响应

许多重要的多组分结晶固体经历机械化学旋节线分解：一种相变，其中成分重新分布与晶体的结构变化相结合，导致动态演化的微观结构。基于这些详细的微观结构快速计算宏观行为的能力对于加速材料发现和设计至关重要。在这里，我们的重点是具有微观结构的材料的宏观非线性弹性响应。由于可以形成的微观结构模式的多样性，人们有兴趣采用纯计算方法来预测它们的宏观响应。然而，宏观的评价，纯粹基于直接数值模拟 (DNS) 的非线性弹性属性在计算上非常昂贵，因此在需要测试大量微观结构时对于材料设计是不切实际的。如果弹性自由能及其随应变的变化是微观结构动力学驱动的总自由能主导轨迹上的小规模波动，则会出现分层性质的进一步复杂性。为了应对这些挑战，我们提出了一种数据驱动的方法，该方法将先进的神经网络 (NN) 模型与 DNS 相结合，以预测在形成微观结构的多组分结晶固体家族中出现的均质、宏观、机械自由能和应力场. 自由能的层次结构'