  Success of machine learning (ML) in the modern world is largely determined by
abundance of data. However at many industrial and scientific problems, amount
of data is limited. Application of ML methods to data-scarce scientific
problems can be made more effective via several routes, one of them is
equivariant neural networks possessing knowledge of symmetries. Here we suggest
that combination of symmetry-aware invariant architectures and stacks of
dilated convolutions is a very effective and easy to implement receipt allowing
sizable improvements in accuracy over standard approaches. We apply it to
representative physical problems from different realms: prediction of bandgaps
of photonic crystals, and network approximations of magnetic ground states. The
suggested invariant multiscale architectures increase expressibility of
networks, which allow them to perform better in all considered cases.
