  Topology Optimization is the process of finding the optimal arrangement of
materials within a design domain by minimizing a cost function, subject to some
performance constraints. Robust topology optimization (RTO) also incorporates
the effect of input uncertainties and produces a design with the best average
performance of the structure while reducing the response sensitivity to input
uncertainties. It is computationally expensive to carry out RTO using finite
element and Monte Carlo sampling. In this work, we use neural network
surrogates to enable a faster solution approach via surrogate-based
optimization and build a Variational Autoencoder (VAE) to transform the the
high dimensional design space into a low dimensional one. Furthermore, finite
element solvers will be replaced by a neural network surrogate. Also, to
further facilitate the design exploration, we limit our search to a subspace,
which consists of designs that are solutions to deterministic topology
optimization problems under different realizations of input uncertainties. With
these neural network approximations, a gradient-based optimization approach is
formed to minimize the predicted objective function over the low dimensional
design subspace. We demonstrate the effectiveness of the proposed approach on
two compliance minimization problems and show that VAE performs well on
learning the features of the design from minimal training data, and that
converting the design space into a low dimensional latent space makes the
problem computationally efficient. The resulting gradient-based optimization
algorithm produces optimal designs with lower robust compliances than those
observed in the training set.
