Accelerating the Computation and Design of Nanoscale Materials with Deep Learning

Abstract

In this article-based thesis, we cover applications of deep learning to different problems in condensed matter physics, where the goal is to either accelerate the computation or design of a nanoscale material. We first motivate and introduce how machine learning methods can be used to accelerate traditional condensed matter physics calculations. In addition, we discuss what designing a material means, and how it has been previously done. We then consider the fundamentals of electronic structure and conventional calculations which include density functional theory (DFT), density functional perturbation theory (DFPT), quantum Monte Carlo (QMC), and electron transport with tight binding. In addition, we cover the basics of deep learning. Afterwards, we discuss 6 articles. The first 5 articles are dedicated to accelerating the computation of nanoscale materials. In Article 1, we use convolutional neural networks to predict energies for diatomic molecules modelled with a Lennard-Jones potential and density functional theory energies of hexagonal lattices with and without defects. In Article 2, we use extensive deep neural networks to represent density functional theory energy functionals for electron gases by using the electron density as input and bypass the Kohn-Sham equations by using the external potential as input. In addition, we use deep convolutional inverse graphics networks to map the external potential directly to the electron density. In Article 3, we use voxel deep neural networks (VDNNs) to map electron densities to kinetic energy densities and functional derivatives of the kinetic energies for graphene lattices. We also use VDNNs to calculate an electron density from a direct minimization calculation and introduce a Monte Carlo based solver that avoids taking a functional derivative altogether. In Article 4, we use a deep learning framework to predict the polarization, dielectric function, Born-effective charges, longitudinal optical transverse optical splitting, Raman tensors, and Raman spectra for 2 crystalline systems. In Article 5, we use VDNNs to map DFT electron densities to QMC energy densities for graphene systems, and compute the energy barrier associated with forming a Stone-Wales defect. In Article 6, we design a graphene-based quantum transducer that has the ability to physically split valley currents by controlling the pn-doping of the lattice sites. The design is guided by an neural network that operates on a pristine lattice and outputs a lattice with pn-doping such that valley currents are optimally split. Lastly, we summarize the thesis and outline future work.