  Recent advances in implicit neural representations show great promise when it
comes to generating numerical solutions to partial differential equations
(PDEs). Compared to conventional alternatives, such representations employ
parameterized neural networks to define, in a mesh-free manner, signals that
are highly-detailed, continuous, and fully differentiable. Most prior works aim
to exploit these benefits in order to solve PDE-governed forward problems, or
associated inverse problems that are defined by a small number of parameters.
In this work, we present a novel machine learning approach to tackle topology
optimization (TO) problems. Topology optimization refers to an important class
of inverse problems that typically feature very high-dimensional parameter
spaces and objective landscapes which are highly non-linear. To effectively
leverage neural representations in the context of TO problems, we use
multilayer perceptrons (MLPs) to parameterize both density and displacement
fields. Using sensitivity analysis with a moving mean squared error, we show
that our formulation can be used to efficiently minimize traditional structural
compliance objectives. As we show through our experiments, a major benefit of
our approach is that it enables self-supervised learning of continuous solution
spaces to topology optimization problems.
