  Deep learning (DL) inverse techniques have increased the speed of artificial
electromagnetic material (AEM) design and improved the quality of resulting
devices. Many DL inverse techniques have succeeded on a number of AEM design
tasks, but to compare, contrast, and evaluate assorted techniques it is
critical to clarify the underlying ill-posedness of inverse problems. Here we
review state-of-the-art approaches and present a comprehensive survey of deep
learning inverse methods and invertible and conditional invertible neural
networks to AEM design. We produce easily accessible and rapidly implementable
AEM design benchmarks, which offers a methodology to efficiently determine the
DL technique best suited to solving different design challenges. Our
methodology is guided by constraints on repeated simulation and an easily
integrated metric, which we propose expresses the relative ill-posedness of any
AEM design problem. We show that as the problem becomes increasingly ill-posed,
the neural adjoint with boundary loss (NA) generates better solutions faster,
regardless of simulation constraints. On simpler AEM design tasks, direct
neural networks (NN) fare better when simulations are limited, while geometries
predicted by mixture density networks (MDN) and conditional variational
auto-encoders (VAE) can improve with continued sampling and re-simulation.
