A deep learning driven uncertain full‐field homogenization method

Abstract

This work is directed to uncertainty quantification of homogenized effective properties of composite materials with a complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as well as in the fiber volume fraction. They are taken into account by multivariate random variables. Uncertainty quantification is carried out by an efficient surrogate model based on pseudospectral polynomial chaos expansion and artificial neural networks, which is trained on a fast Fourier transformation based homogenization method. The numerical example deals with the comparison of the presented method to Monte Carlo-type simulation for uncertain homogenization of spherical inclusions in a matrix material.

Physics informed neural networks for continuum micromechanics

“…In a former work the problem was tackled using supervised machine learning with artificial neural networks (ANN) [1,2].…”