机器学习材料物理：多分辨率神经网络学习演化微结构的自由能与非线性弹性响应
Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
AI总结：
针对含微结构多组元晶体宏观弹性响应计算成本高的问题，提出结合DNS与多分辨率KBNN的数据驱动方法，采用预训练DNN/CNN表征层级演化自由能，预测宏观力学自由能与应力场。
摘要：
许多重要的多组元晶体会发生力化学旋节分解：这是一种成分再分布与晶体结构变化相耦合的相变过程，会形成动态演化的微结构。基于这些精细微结构快速计算宏观行为的能力，对于加速材料发现与设计至关重要。本研究聚焦于含微结构材料的宏观非线性弹性响应。由于可形成的微结构图案具有多样性，研究界有兴趣采用纯计算方法预测其宏观响应。然而，仅基于直接数值模拟（DNS）评估宏观非线性弹性属性的计算成本极高，因此在需要测试大量微结构的材料设计场景中并不实用。如果弹性自由能及其随应变的变化只是微结构动力学驱动的总自由能主导轨迹上的小尺度涨落，还会进一步产生层级性的复杂问题。为应对这些挑战，我们提出了一种数据驱动方法，将先进的神经网络（NN）模型与DNS相结合，用于预测一类会形成微结构的多组元晶体中产生的均质化宏观力学自由能与应力场。自由能演化的层级结构为该机器学习范式赋予了多分辨率特性：我们构建了基于知识的神经网络（KBNN），采用预训练的全连接深度神经网络（DNN）或预训练的卷积神经网络（CNN）来描述数据的主导特征，以完整表征层级演化的自由能。
英文摘要：
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.
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