  Fluid-flow devices with low dissipation, but high contact area, are of
importance in many applications. A well-known strategy to design such devices
is multi-scale topology optimization (MTO), where optimal microstructures are
designed within each cell of a discretized domain. Unfortunately, MTO is
computationally very expensive since one must perform homogenization of the
evolving microstructures, during each step of the homogenization process. As an
alternate, we propose here a graded multiscale topology optimization (GMTO) for
designing fluid-flow devices. In the proposed method, several pre-selected but
size-parameterized and orientable microstructures are used to fill the domain
optimally. GMTO significantly reduces the computation while retaining many of
the benefits of MTO.
  In particular, GMTO is implemented here using a neural-network (NN) since:
(1) homogenization can be performed off-line, and used by the NN during
optimization, (2) it enables continuous switching between microstructures
during optimization, (3) the number of design variables and computational
effort is independent of number of microstructure used, and, (4) it supports
automatic differentiation, thereby eliminating manual sensitivity analysis.
Several numerical results are presented to illustrate the proposed framework.
