  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.
