Date of Award


Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Mechanical Engineering-Engineering Mechanics (PhD)

Administrative Home Department

Department of Mechanical Engineering-Engineering Mechanics

Advisor 1

Susanta Ghosh

Committee Member 1

Amartya Banerjee

Committee Member 2

Ranjit Pati

Committee Member 3

Soumik Sarkar


Kohn-Sham density functional theory is the work horse of computational material science research. The core of Kohn-Sham density functional theory, the Kohn-Sham equations, output charge density, energy levels and wavefunctions. In principle, the electron density can be used to obtain several other properties of interest including total potential energy of the system, atomic forces, binding energies and electric constants. In this work we present machine learning models designed to bypass the Kohn-Sham equations by directly predicting electron density. Two distinct models were developed: one tailored to predict electron density for quasi one-dimensional materials under strain, while the other is applicable across a wide array of material systems, with a specific emphasis on metallic and alloy compositions.

The first model applies to important classes of material systems such as nanotubes, for which, tuning the interplay of mechanical deformations and electronic fields --- i.e., strain engineering --- is an active area of investigation. Using armchair single wall carbon nanotubes as a example, we demonstrate the use of the model to predict ground state electron density and the nuclear pseudocharges, when three parameters --- namely, the radius of the nanotube, its axial stretch, and the twist per unit length --- are specified as inputs. Other electronic properties of interest, including the ground state electronic free energy, can be evaluated from these predicted fields with low-overhead post-processing, typically to chemical accuracy. We anticipate that this framework will find utility in the automated discovery of low--dimensional materials, as well as the multi-scale modeling of such systems.

The second model has an emphasis on metallic and alloy systems. One of the fundamental challenge for this model is generation of training data. The computational expense of KS-DFT scales cubically with system size which tends to stymie training data generation, making it difficult to develop quantifiably accurate ML models that are applicable across many scales and system configurations. Here, we address this fundamental challenge by employing transfer learning to leverage the multi-scale nature of the training data, while comprehensively sampling system configurations using thermalization. Our ML models are less reliant on heuristics, and being based on Bayesian neural networks, enable uncertainty quantification. We show that our models incur significantly lower data generation costs while allowing confident --- and when verifiable, accurate --- predictions for a wide variety of bulk systems well beyond training, including systems with defects, different alloy compositions, and at unprecedented, multi-million-atom scales. Moreover, such predictions can be carried out using only modest computational resources.