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A Comparison Of Quaternion Neural Network Backpropagation Algorithms, Jeremiah Bill, Bruce A. Cox, Lance Champaign Jun 2023

A Comparison Of Quaternion Neural Network Backpropagation Algorithms, Jeremiah Bill, Bruce A. Cox, Lance Champaign

Faculty Publications

This research paper focuses on quaternion neural networks (QNNs) - a type of neural network wherein the weights, biases, and input values are all represented as quaternion numbers. Previous studies have shown that QNNs outperform real-valued neural networks in basic tasks and have potential in high-dimensional problem spaces. However, research on QNNs has been fragmented, with contributions from different mathematical and engineering domains leading to unintentional overlap in QNN literature. This work aims to unify existing research by evaluating four distinct QNN backpropagation algorithms, including the novel GHR-calculus backpropagation algorithm, and providing concise, scalable implementations of each algorithm using a …


Investigation And Statistical Modeling Of The Mechanical Properties Of Additively Manufactured Lattices, Derek G. Spear, Anthony N. Palazotto Jul 2021

Investigation And Statistical Modeling Of The Mechanical Properties Of Additively Manufactured Lattices, Derek G. Spear, Anthony N. Palazotto

Faculty Publications

This paper describes the background, test methodology, and experimental results associated with the testing and analysis of quasi-static compression testing of additively manufactured open-cell lattice structures. The study aims to examine the effect of lattice topology, cell size, cell density, and surface thickness on the mechanical properties of lattice structures. Three lattice designs were chosen, the Diamond, I-WP, and Primitive Triply Periodic Minimal Surfaces (TPMSs). Uniaxial compression tests were conducted for every combination of the three lattice designs, three cell sizes, three cell densities, and three surface thicknesses. In order to perform an efficient experiment and gain the most information …