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.

High-entropy alloys possessing mechanical, chemical, and electrical properties that far exceed those of conventional alloys have the potential to make a significant impact on many areas of engineering. Identifying element combinations and configurations to form these alloys, however, is a difficult, time-consuming, computationally intensive task. Machine learning has revolutionized many different fields due to its ability to generalize well to different problems and produce computationally efficient, accurate predictions regarding the system of interest. In this thesis, we demonstrate the effectiveness of machine learning models applied to toy cases representative of simplified physics that are relevant to high-entropy alloy simulation. We show these models are effective at learning nonlinear dynamics for single and multi-particle cases and that more work is needed to accurately represent complex cases in which the system dynamics are chaotic. This thesis serves as a demonstration of the potential benefits of machine learning applied to high-entropy alloy simulations to generate fast, accurate predictions of nonlinear dynamics.

Titanium has been and continues to be a popular metal across any form of manufacturing and production because of its extremely favorable properties. In important circumstances, it finds itself outclassing many metals by being lighter and less dense than comparably strong metals like steel. Relative to other metals it has a noteworthy corrosion resistance as it is stable when it oxidizes, and due to the inert nature of the metal, it is famously hypoallergenic and as a result used in a great deal of aviation and medical fields, including being used to produce replacement joints, with the notable limitation of the material being its cost of manufacturing. Among the variants of the metal and alloys used, Ti6Al4V alloy is famous for being the most reliable and popular combination for electron beam manufacturing(EBM) as a method of additive manufacturing. <br/>Developed by the Swedish Arcam, AB, EBM is one of the more recent methods of additive manufacturing, and is notable for its lack of waste by combining most of the material into the intended product due to its precision. This method, much like the titanium it is used to print in this case, is limited mostly by time and value of production. <br/>For this thesis, nine different simulations of a dogbone model were generated and analyzed in Ansys APDL using finite element analysis at various temperature and print conditions to create a theoretical model based on experimentally produced values.