Material optimization (e.g., texture optimization) and multi-scale modeling (e.g., FE^2) of materials requires numerous instances (realizations) of the same calculations. The governing equations of these problems are highly non-linear (because of the complex material behavior and microstructure) and requires enormous computational power and time to solve due to its high dimensional nature (e.g., a typical RVE calculation is a mapping from 256^3 to 256^3 dimensions).
In the current study, we develop machine learning based methods to replace the expensive calculations with inexpensive acceptable approximations. To this end, we treat the calculation as an input output map and seek to learn an approximation of this map by a combination of PCA/Auto-Encoder based reduced order modeling and deep neural network. The approach is demonstrated on poly-crystalline RVE with anisotropic elasticity and crystal plasticity. It is shown that the map can be efficiently learned by our approach and the approximation error is bounded and monotonically decreasing with increasing number of training samples.
