Invariant multiscale neural networks for data-scarce scientific applications

TL;DR

This paper introduces invariant multiscale neural networks that leverage symmetry-awareness and dilated convolutions to improve data efficiency and accuracy in scientific applications with limited data.

Contribution

It proposes a novel combination of invariant architectures and dilated convolutions, enhancing neural network performance in data-scarce scientific problems.

Findings

Significant accuracy improvements over standard methods.

Effective in predicting photonic crystal bandgaps.

Accurate network approximations of magnetic ground states.

Abstract

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.