论文标题
机器学习材料物理：多分辨率神经网络学习不断发展的微观结构的自由能和非线性弹性响应
Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
论文作者
论文摘要
许多重要的多组分晶体固体都会发生机械化学旋转分解：一个相变的相变，其中组成重新分布与晶体的结构变化相结合，从而导致动态发展的微结构。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。由于可能形成的微观结构模式的多样性，因此有兴趣采用纯计算方法来预测其宏观响应。但是，纯粹基于直接数值模拟（DNS）的宏观，非线性弹性特性的评估在计算上非常昂贵，因此，当需要测试大量微结构时，对于材料设计而言，对材料设计的不切实际。如果弹性自由能及其与应变变化是对由微结构动力学驱动的总自由能的主要轨迹的小规模波动，则会出现层次结构的进一步复杂性。为了应对这些挑战，我们提出了一种数据驱动的方法，该方法将高级神经网络（NN）模型与DNS相结合，以预测在多组分晶体固体家族中产生的均质，宏观，机械自由能和应力场，这些固体产生了微观结构。自由能的演化的层次结构诱导了机器学习范式的多分辨率特征：我们构建基于知识的神经网络（KBNN），具有预先训练的完全连接的深度神经网络（DNN），或者预先培训的卷积神经网络（CNN），以描述该数据的主要能量，以表明该数据的主要功能，以表明该数据的主要功能，以表明该数据的主要能量完全均能供应。
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.
