  Optical interactions have an important impact on the optical response of
nanostructures in complex environments. Accounting for interactions in large
ensembles of structures requires computationally demanding numerical
calculations. In particular if no periodicity can be exploited, full field
simulations can become prohibitively expensive. Here we propose a method for
the numerical description of aperiodic assemblies of plasmonic nanostructures.
Our approach is based on dressed polarizabilities, which are conventionally
very expensive to calculate, a problem which we alleviate using a deep
convolutional neural network as surrogate model. We demonstrate that the method
offers high accuracy with errors in the order of a percent. In cases where the
interactions are predominantly short-range, e.g. for out-of-plane illumination
of planar metasurfaces, it can be used to describe aperiodic metasurfaces of
basically unlimited size, containing many thousands of unordered plasmonic
nanostructures. We furthermore show that the model is capable to spectrally
resolve coupling effects. The approach is therefore of highest interest for the
field of metasurfaces. It provides significant advantages in applications like
homogenization of large aperiodic planar metastructures or the design of
sophisticated wavefronts at the micrometer scale, where optical interactions
play a crucial role.
