  When deformation gradients act on the scale of the microstructure of a part
due to geometry and loading, spatial correlations and finite-size effects in
simulation cells cannot be neglected. We propose a multiscale method that
accounts for these effects using a variational autoencoder to encode the
structure-property map of the stochastic volume elements making up the
statistical description of the part. In this paradigm the autoencoder can be
used to directly encode the microstructure or, alternatively, its latent space
can be sampled to provide likely realizations. We demonstrate the method on
three examples using the common additively manufactured material AlSi10Mg in:
(a) a comparison with direct numerical simulation of the part microstructure,
(b) a push forward of microstructural uncertainty to performance quantities of
interest, and (c) a simulation of functional gradation of a part with
stochastic microstructure.
