Design and exploration of strongly correlated systems through machine learning computational acceleration

Predicting material properties from an ab-initio perspective has long been the goal of computational physics. Correlated materials, however, are difficult to simulate given the complexity that arises from electron-electron interactions. While conventional Kohn-Sham DFT provides a good starting point, it often fails when dealing with materials hosting strong dynamical correlation effects. Electronic structure calculations of strongly interacting systems require deeper calculations. Given the computational cost however, it is currently difficult to utilize these techniques at a large scale. Additional techniques must be developed to make computations tractable. There is also a need to design from first principles strongly correlated systems that can serve as an experimental testbed for various many-body phenomena. This dissertation explores the topic of accelerating the calculations of strongly correlated materials using machine learning techniques as well as designing a new testbed platform for strongly correlated systems. The first chapter introduces the challenges faced and provides an overview of the methodologies used to address these challenges. In chapter 2, we focus on the design and investigation of two novel systems, one weakly correlated and one strongly correlated. We explore systematically the design of epitaxially strained perovskite oxynitrides and the design of novel heavy fermion compounds within a Boron-Carbon clathrate framework. Chapter 3 introduces machine learned interatomic potentials, where we utilize them to massively speedup the computations of phase transition pathways for correlated Ce and to find the melting curve of NiO. For chapter 4, we focus on using equivariant graph neural networks for the direct prediction of self-energy. Chapter 5 examines the integration of all these techniques to perform a large-scale molecular dynamics simulation of Fe at Earth's core conditions. Finally, chapter 6 develops a diffusion model-based approach to denoise imaginary time Green's functions, which are used to accelerate the DMFT self-consistency loop. The results show clearly that machine learning can massively accelerate the calculations of strongly correlated systems. The work in this dissertation provides multiple perspectives into the techniques by which machine learning can be used for this purpose, pushing forward the accessible space of materials discovery.