Hamilton-Jacobi (HJ) reachability is commonly used to determine Safe Flight Envelopes (SFEs), yet it is often limited by the "curse of dimensionality". While Deep Neural Network (DNN)-based solvers like DeepReach mitigate scaling issues, they remain computationally and memory-intensive.

This paper introduces KANReach, a novel solver that leverages Kolmogorov-Arnold Networks (KANs) with B-spline activation functions for grid-free reachable set estimation. The architecture is evaluated using three case studies: a first-order regulator, a double integrator, and a 3D Dubins car. Benchmarking against DeepReach reveals that at comparable model sizes, KANReach achieves superior accuracy via Value Function Regression (VFR). However, it currently faces difficulties in Physics-Informed Learning (PIL) that limit its training efficiency relative to traditional DNNs. Additionally, this paper proposes Absolute Maximum Error Bounding (AMEB), a technique that exploits the unique convex-hull property of B-splines to derive formal safety guarantees that verify the computed SFE.

The goal of project Altus is to do an in-situ investigation of Polar Mesospheric Clouds (PMCs). These clouds form around an altitude of 84 km, and only for 60 to 80 days per year, during the summer. Normally, these clouds only form in the polar regions, from around 50◦ latitude north and south. Recently, however, PMCs have been observed as low as 40◦ north. There are theories linking this change in location, and other unexpected behaviours of PMCs, to climate change. However, further research is still required to confirm these theories. As these changes are happening at a slow rate, a database of PMC measurements would be extremely beneficial to track indicator values over time. Project Altus sets out to bridge this knowledge gap by taking regular measurements of PMCs over an extended period of time.