In Condensed Matter Physics, the computational expense to evaluate the total potential energy of a collection of atoms using standard ab initio methods is typically large. This limits the scale of phenomena that can be studied in both length and time. Data-driven techniques have established a pragmatic extension to ab initio calculations, balancing reductions in the calculation time with potential losses of accuracy in the properties of interest. Both paradigms compliment one another and when used appropriately, are valuable tools that enable and stimulate research in Materials Science. Unlike traditional efforts, modern techniques to include data employ flexible functional forms, extending the applicability of such methods to a diverse range of physical quantities. Recently, interest in utilising data in total energy calculations has turned towards the electron density. With an electron density that is close to the ground state, data-derived kinetic energy functionals in orbital-free density functional theory can be applied to evaluate the total energy without using gradients of the functional with respect to the electron density. For this purpose, a number of approaches to calculate data-derived densities have been proposed in recent years.

In this thesis, we begin by reviewing several fixed-form expressions to approximate the potential energy of hexagonal layered crystals and show how a flexible form is essential to fully utilise the available data. We then focus on developing new approaches to approximate ground state electron densities and on novel applications that help to further unify data-driven and ab initio techniques within electronic structure. By calculating reliable uncertainty estimates, we show that data-derived densities can be incorporated into density functional theory in a “safe” manner. We also show that with accurate initial densities and for systems that otherwise have a poor initial estimate, we can reduce the number of self-consistent field iterations that are necessary to reach self-consistency in Kohn-Sham density functional theory. We hope that the work in this thesis will contribute to improving initial states in density functional theory, support the application of data-derived orbital-free kinetic energy functionals and encourage an ever closer and mutually beneficial cohesion between data-driven and ab initio techniques throughout the Natural Sciences.