Developing Density Functional Theory with Physical Prior Knowledge

Density functional theory (DFT) has been used extensively over the past several decades and across many branches of science. The success of DFT lies in its relatively low-cost and usefully high accuracy in many practical systems of interest. However, there are still many instances, such as strongly correlated systems or systems at high temperatures, where conventional DFT approaches are no longer reliable. In addition, reliable DFT approaches are often computationally intractable for large system sizes, limiting their scope of application in realistic system settings. This dissertation is a collection of my contributions to address these fundamental challenges in the field. A common theme across all projects is the use of physical prior knowledge to motivate or (in)directly constrain the methods and techniques developed. In Chapter 1, I provide context for the research presented in the following self-contained chapters. Chapter 2 introduces condition probability DFT (CP-DFT) as a new and alternative density functional approach to obtain conditional probability densities and ground-state energies. Chapter 3 expands upon the previous chapter by establishing CP-DFT as a formally exact theory and derives several key physical properties of CP densities and corresponding potentials used in the theory. Chapter 4 analyzes and discusses the role of exact physical conditions (constraints) in developing conventional Kohn-Sham DFT exchange-correlation (XC) approximations. Chapter 5 introduces the Kohn-Sham regularizer method for training neural network-based XC models for strongly correlated systems. Chapter 6 expands on the previous chapter by developing a spin-adapted Kohn-Sham regularizer and demonstrating impressive generalizability on weakly correlated systems. Finally, Chapter 7 explores the repurposing of Tensor Processing Units – hardware designed for machine-learning tasks – for large-scale DFT calculations by utilizing algorithms that exploit physical properties of the density matrix.

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