The research presented in this Honors Thesis provides development in machine learning models which predict future states of a system with unknown dynamics, based on observations of the system. Two case studies are presented for (1) a non-conservative pendulum and (2) a differential game dictating a two-car uncontrolled intersection scenario. In the paper we investigate how learning architectures can be manipulated for problem specific geometry. The result of this research provides that these problem specific models are valuable for accurate learning and predicting the dynamics of physics systems.<br/><br/>In order to properly model the physics of a real pendulum, modifications were made to a prior architecture which was sufficient in modeling an ideal pendulum. The necessary modifications to the previous network [13] were problem specific and not transferrable to all other non-conservative physics scenarios. The modified architecture successfully models real pendulum dynamics. This case study provides a basis for future research in augmenting the symplectic gradient of a Hamiltonian energy function to provide a generalized, non-conservative physics model.<br/><br/>A problem specific architecture was also utilized to create an accurate model for the two-car intersection case. The Costate Network proved to be an improvement from the previously used Value Network [17]. Note that this comparison is applied lightly due to slight implementation differences. The development of the Costate Network provides a basis for using characteristics to decompose functions and create a simplified learning problem.<br/><br/>This paper is successful in creating new opportunities to develop physics models, in which the sample cases should be used as a guide for modeling other real and pseudo physics. Although the focused models in this paper are not generalizable, it is important to note that these cases provide direction for future research.

With the extreme strides taken in physics in the early twentieth century, one of the biggest questions on the minds of scientists was what this new branch of quantum physics would be able to be used for. The twentieth century saw the rise of computers as devices that significantly aided in calculations and performing algorithms. Because of the incredible success of computers and all of the groundbreaking possibilities that they afforded, research into using quantum mechanics for these systems was proposed. Although theoretical at the time, it was found that a computer that had the ability to leverage quantum mechanics would be far superior to any classical machine. This sparked a wave of interest in research and funding in this exciting new field. General-use quantum computers have the potential to disrupt countless industries and fields of study, like physics, medicine, engineering, cryptography, finance, meteorology, climatology, and more. The supremacy of quantum computers has not yet been reached, but the continued funding and research into this new technology ensures that one day humanity will be able to unlock the full potential of quantum computing.