Tight-binding deep learning approach to band structures calculations

Band structures are ubiquitous in physics as they describe natural as well as engineered materials. Even for systems for which the numerical calculation of the band structure for a single configuration is in itself not proibitevely expensive, efficient numerical methods are highly valuable as they allow the systematic investigation of large sets of configurations. This is often required because configuration spaces are typically huge.

In this talk we present a numerical method for band structure calculations that is based on deep neural networks (NNs). In our approach, the NN does not predict the band structure directly but rather makes it easily accessible via the parameters of a tight-binding model. This is, thus, an example of so-called known-operator learning.

Our tight-binding learning NN goes beyond other existing NN based approaches to band structure calculations in that: (i) It does not focus on a few selected model parameters but rather provides a full mapping from arbitrary unit cell geometry to bands. (ii) It allows to better interpret the network's predictions. (iii) It gives access to the space-group symmetries of the underlying normal modes (especially important for topological systems).