Exploring band topology of engineered materials using deep neural networks

This talk focuses on the first applications of our deep Neural Network (NN) based approach to band structure calculations. A distinctive feature of our approach is that our NN does not predict the band structure directly but rather learns to predict the parameters of an auxiliary Tight-Binding (TB) model. This TB model gives then access not only to the band structure but also to the topological properties of the Bloch waves.
The applications we consider are geared towards engineered materials such as photonic and phononic crystals in that we use as an input of our neural network the unit cell geometry. We demonstrate the use of our NN to perform efficiently the statistical analysis of the topological properties of selected distributions of potentials. Our analysis is based on recent break-throughs in the understanding of band structure topology and ties to the the systematic classification of all natural materials based on their electronic topological properties (sometimes known as Topological Quantum Chemistry). Moreover, we demonstrate the use of our NN for optimization (random or gradient based) of band structures in the design of (i) band inversions, (ii) physical implementations of fragile topology, (iii) physical implementations of selected topological TB models.