  Multiscale topology optimization (M-TO) entails generating an optimal global
topology, and an optimal set of microstructures at a smaller scale, for a
physics-constrained problem. With the advent of additive manufacturing, M-TO
has gained significant prominence. However, generating optimal microstructures
at various locations can be computationally very expensive. As an alternate,
graded multiscale topology optimization (GM-TO) has been proposed where one or
more pre-selected and graded (parameterized) microstructural topologies are
used to fill the domain optimally. This leads to a significant reduction in
computation while retaining many of the benefits of M-TO.
  A successful GM-TO framework must: (1) be capable of efficiently handling
numerous pre-selected microstructures, (2) be able to continuously switch
between these microstructures during optimization, (3) ensure that the
partition of unity is satisfied, and (4) discourage microstructure mixing at
termination.
  In this paper, we propose to meet these requirements by exploiting the unique
classification capacity of neural networks. Specifically, we propose a graded
multiscale topology optimization using neural-network (GM-TOuNN) framework with
the following features: (1) the number of design variables is only weakly
dependent on the number of pre-selected microstructures, (2) it guarantees
partition of unity while discouraging microstructure mixing, and (3) it
supports automatic differentiation, thereby eliminating manual sensitivity
analysis. The proposed framework is illustrated through several examples.
