Theses and Dissertations
Graph neural networks (GNN) offer a potential method of bypassing the Kohn-Sham equations in density functional theory (DFT) calculations by learning both the Hohenberg-Kohn (HK) mapping of electron density to energy, allowing for calculations of much larger atomic systems and time scales and enabling large-scale MD simulations with DFT-level accuracy. In this work, we investigate the feasibility of GNNs to learn the HK map from the external potential approximated as Gaussians to the electron density 𝑛(𝑟), and the mapping from 𝑛(𝑟) to the energy density 𝑒(𝑟) using Pytorch Geometric. We develop a graph representation for densities on radial grid points and determine that a k-nearest neighbor algorithm for determining node connections is an effective approach compared to a distance cutoff model, having an average graph size of 6.31 MB and 32.0 MB for datasets with 𝑘 = 10 and 𝑘 = 50 respectively. Furthermore, we develop two GNNs in Pytorch Geometric, and demonstrate a decrease in training losses for a 𝑛(𝑟) to 𝑒(𝑟) of 8.52 · 10^14 and 3.10 · 10^14 for 𝑘 = 10 and 𝑘 = 20 datasets respectively, suggesting the model could be further trained and optimized to learn the electron density to energy functional.
The importance of nonverbal communication has been well established through several theories including Albert Mehrabian's 7-38-55 rule that proposes the respective importance of semantics, tonality and facial expressions in communication. Although several studies have examined how emotions are expressed and preceived in communication, there is limited research investigating the relationship between how emotions are expressed through semantics and facial expressions. Using a facial expression analysis software to deconstruct facial expressions into features and a K-Nearest-Neighbor (KNN) machine learning classifier, we explored if facial expressions can be clustered based on semantics. Our findings indicate that facial expressions can be clustered based on semantics and that there is an inherent congruence between facial expressions and semantics. These results are novel and significant in the context of nonverbal communication and are applicable to several areas of research including the vast field of emotion AI and machine emotional communication.