Learning the Local Density of States of a Bilayer Moire Material
Diyi Liu, Alexander B. Watson, Michael Hott, Stephen Carr, Mitchell Luskin · Multiscale Modeling and Simulation · 2025
Abstract. Recent work of three of the authors showed that the operator which maps the local density of states of a one-dimensional untwisted bilayer material to the local density of states of the same bilayer material at nonzero twist, known as the twist operator, can be learned by a neural network. In this work, we first provide a mathematical formulation of that work, making precise the relevant models and operator learning problem. We then prove that the operator learning problem is well-posed for a family of one-dimensional models. To do this, we first prove existence and regularity of the twist operator by solving an inverse problem. We then invoke the universal approximation theorem for operators to prove the existence of a neural network capable of approximating the twist operator.