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.

Oscillatory perturbations with varying amplitudes and frequencies have been found to significantly affect human standing balance. However, previous studies have only applied perturbation in either the anterior-posterior (AP) or the medio-lateral (ML) directions. Little is currently known about the impacts of 2D oscillatory perturbations on postural stability, which are more commonly seen in daily life (i.e., while traveling on trains, ships, etc.). This study investigated the effects of applying 2D perturbations vs 1D perturbations on standing stability, and how increasing the frequency and amplitude of perturbation impacts postural stability. A dual-axis robotic platform was utilized to simulate various oscillatory perturbations and evaluate standing postural stability. Fifteen young healthy subjects were recruited to perform quiet stance on the platform. Impacts of perturbation direction (i.e., 1D versus 2D), amplitude, and frequency on postural stability were investigated by analyzing different stability measures, specifically AP/ML/2D Center-of-Pressure (COP) path length, AP/ML/2D Time-to-Boundary (TtB), and sway area. Standing postural stability was compromised more by 2D perturbations than 1D perturbations, evidenced by a significant increase in COP path length and sway area and decrease in TtB. Further, the stability decreased as 2D perturbation amplitude and frequency increased. A significant increase in COP path length and decrease in TtB were consistently observed as the 2D perturbation amplitude and frequency increased. However, sway area showed a considerable increase only with increasing perturbation amplitude but not with increasing frequency.