  Microstructural heterogeneity affects the macro-scale behavior of materials.
Conversely, load distribution at the macro-scale changes the microstructural
response. These up-scaling and down-scaling relations are often modeled using
multiscale finite element (FE) approaches such as FE-squared ($FE^2$). However,
$FE^2$ requires numerous calculations at the micro-scale, which often renders
this approach intractable. This paper reports an enormously faster machine
learning (ML) based approach for multiscale mechanics modeling. The proposed
ML-driven multiscale analysis approach uses an ML-model that predicts the local
stress tensor fields in a linear elastic fiber-reinforced composite
microstructure. This ML-model, specifically a U-Net deep convolutional neural
network (CNN), is trained separately to perform the mapping between the spatial
arrangement of fibers and the corresponding 2D stress tensor fields. This
ML-model provides effective elastic material properties for up-scaling and
local stress tensor fields for subsequent down-scaling in a multiscale analysis
framework. Several numerical examples demonstrate a substantial reduction in
computational cost using the proposed ML-driven approach when compared with the
traditional multiscale modeling approaches such as full-scale FE analysis, and
homogenization based $FE^2$ analysis. This approach has tremendous potential in
efficient multiscale analysis of complex heterogeneous materials, with
applications in uncertainty quantification, design, and optimization.
