  Surrogate models for partial-differential equations are widely used in the
design of meta-materials to rapidly evaluate the behavior of composable
components. However, the training cost of accurate surrogates by machine
learning can rapidly increase with the number of variables. For photonic-device
models, we find that this training becomes especially challenging as design
regions grow larger than the optical wavelength. We present an active learning
algorithm that reduces the number of training points by more than an order of
magnitude for a neural-network surrogate model of optical-surface components
compared to random samples. Results show that the surrogate evaluation is over
two orders of magnitude faster than a direct solve, and we demonstrate how this
can be exploited to accelerate large-scale engineering optimization.
