To address the growing demands of operating in the space domain, the U.S. Space Force and space domain awareness (SDA) operators must determine how to prioritize sensor observations more effectively, scale up to meet the sheer volume of resident space objects, and develop analytic capabilities that reflect the complexity of orbital mechanics and space operations, all while maintaining the responsiveness necessitated by operations in a warfighting domain. Although artificial intelligence and machine learning (AI/ML) tools have the potential to help meet these SDA challenges, the impact of these tools on the overall success of the SDA mission is not well understood, and this lack of understanding is a barrier to plan for and optimize the integration of these tools. This report documents technical approaches to demonstrating the feasibility of AI/ML when applied to the U.S. Space Force and the space domain awareness mission. The ability to estimate the current and future states and uncertainties of a resident space object using mathematical and numerical techniques is fundamental for current SDA processes. The authors tested AI/ML algorithms, particularly Bayesian neural networks, to determine their suitability for these tasks. The research presented in this report focuses on the highly resource-intensive conjunction assessment mission under the broader SDA mission set. The two case studies focus on prediction and classification capabilities of neural networks and the use of these capabilities to improve the conjunction assessment. The authors found that Bayesian neural networks offer suitable performance trade-offs on metrics most likely to be relevant to risk-based SDA decisionmaking when compared with traditional processes and greater performance on metrics when compared with standard neural networks.