Modeling the Band Structure of Periodic Crystals with Physics-Informed Neural Networks

Accurate computation of the electronic band structure is important for understanding material properties. Traditional methods, such as density functional theory, are highly successful but become computationally costly for large systems. We propose a neural network architecture to model the wavefunction and band structure of a periodic crystal. This type of Physics-Informed Neural Network (PINN) solves the Schrödinger equation using a data-free approach. We apply our network to a series of 1-dimensional potentials, demonstrating accurate prediction of the Bloch wavefunctions and band structures when compared to numerically computed solutions. Finally, we demonstrate how our approach allows for further generalization, and discuss the future of our approach.