Data-driven approximations of topological insulator systems

A data-driven approach to calculating tight-binding models for discrete coupled-mode systems is presented. Specifically, spectral and topological data is used to build an appropriate discrete model that accurately replicates these properties. This work is motivated by topological insulator systems that are often described by tight-binding models. The problem is formulated as the minimization of an appropriate residual (objective) function. Given bulk spectral data and a topological index (e.g. winding number), an appropriate discrete model is obtained to arbitrary precision. A nonlinear least squares method is used to determine the coefficients. The effectiveness of the scheme is highlighted against a Schr\"odinger equation with a periodic potential that can be described by the Su-Schrieffer-Heeger model.