Data Driven for Homogenization

Developed by the Computational Physics Group at the University of Michigan. http://www.umich.edu/~compphys/index.html

List of contributors:
Xiaoxuan Zhang
Krishna Garikipati

Overview

This repo contains code for generating the results reported in the reference, where 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 microstructures are numerically generated by solving a coupled, mechanochemical spinodal decomposition problem governed by nonlinear strain gradient elasticity and the Cahn-Hilliard phase field equation, which is solved by the mechanoChemIGA code developed in the same group. A 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. 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. We demonstrate multi-resolution learning of the materials physics; specifically of the nonlinear elastic response for both fixed and evolving microstructures.

Reference

If you write a paper using results obtained with the help of this code, please consider citing the following work:

"Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures" (arXiv preprint arXiv:2001.01575)
X. Zhang, K. Garikipati

@article{Zhang+Garikipati+2020-MLHomogenization,
  Title                    = {Machine learning materials physics: Multi-resolution  neural networks learn the free energy and nonlinear elastic response of evolving microstructures},
  Author                   = {X. Zhang and K. Garikipati},
  Journal                  = {arXiv preprint arXiv:2001.01575},
  Year                     = {2020},
}