Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
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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 dynamic and intricate microstructures. The ability to rapidly compute the macroscopic behavior based on these detailed microstructures is of paramount importance for accelerating material discovery and design. 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 mechanical free energy and homogenized stress fields on microstructures in a family of two-dimensional multi-component crystalline solids. The microstructres are numerically generated by solving a coupled, Cahn-Hilliard and nonlinear strain gradient elasticity problem. 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 feature of the data to fully represent the hierarchichally evolving free energy. We demonstrate multi-resolution learning of the materials physics of nonlinear elastic response for both fixed and evolving microstructures.
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