Modern cyber-physical systems — such as autonomous vehicles, medical devices, and power grid controllers — must operate safely despite uncertainty in their environments, models, and decision-making components. A key challenge in ensuring their safety is predicting all possible future behaviors of these systems to verify that unsafe conditions are avoided. Doing so, in practice, allows us to encounter unforeseen and potentially dangerous behaviors in these systems. This problem, known as reachability analysis, is central to the design and certification of safety-critical systems. However, existing methods struggle to scale to complex, nonlinear systems and are especially challenged when systems incorporate artificial intelligence (AI) components. This project addresses a fundamental gap by developing new mathematical and computational tools for analyzing such systems under uncertainty. The proposed advances will improve the ability to provide strong safety guarantees for emerging technologies, particularly AI-enabled autonomous systems that are increasingly deployed in domains critical to national health, economic prosperity, and public safety. By enabling more reliable verification of these systems, the project contributes to safer transportation, more robust medical technologies, and resilient infrastructure. In addition to its research contributions, the project will support education and workforce development through open-source software, benchmark problems, and a summer s