Sample-Free Safety Assessment of Neural Network Controllers via Taylor Methods

In recent years, artificial neural networks have been increasingly studied as feedback controllers for guidance problems. While effective in complex scenarios, they lack the verification guarantees found in classical guidance policies. Their black-box nature creates significant concerns regarding trustworthiness, limiting their adoption in safety-critical spaceflight applications. This work addresses this gap by developing a method to assess the safety of a trained neural network feedback controller via automatic domain splitting and polynomial bounding. The methodology involves embedding the trained neural network into the system's dynamical equations, rendering the closed-loop system autonomous. The system flow is then approximated by high-order Taylor polynomials, which are subsequently manipulated to construct polynomial maps that project state uncertainties onto an event manifold. Automatic domain splitting ensures the polynomials are accurate over their relevant subdomains, whilst also allowing an extensive state-space to be analysed efficiently. Utilising polynomial bounding techniques, the resulting event values may be rigorously constrained and analysed within individual subdomains, thereby establishing bounds on the range of possible closed-loop outcomes from using such neural network controllers and supporting safety assessment and informed operational decision-making in real-world missions.

Can LLMs Do Rocket Science? Exploring the Limits of Complex Reasoning with GTOC 12

Large Language Models (LLMs) have demonstrated remarkable proficiency in code generation and general reasoning, yet their capacity for autonomous multi-stage planning in high-dimensional, physically constrained environments remains an open research question. This study investigates the limits of current AI agents by evaluating them against the 12th Global Trajectory Optimization Competition (GTOC 12), a complex astrodynamics challenge requiring the design of a large-scale asteroid mining campaign. We adapt the MLE-Bench framework to the domain of orbital mechanics and deploy an AIDE-based agent architecture to autonomously generate and refine mission solutions. To assess performance beyond binary validity, we employ an "LLM-as-a-Judge" methodology, utilizing a rubric developed by domain experts to evaluate strategic viability across five structural categories. A comparative analysis of models, ranging from GPT-4-Turbo to reasoning-enhanced architectures like Gemini 2.5 Pro, and o3, reveals a significant trend: the average strategic viability score has nearly doubled in the last two years (rising from 9.3 to 17.2 out of 26). However, we identify a critical capability gap between strategy and execution. While advanced models demonstrate sophisticated conceptual understanding, correctly framing objective functions and mission architectures, they consistently fail at implementation due to physical unit inconsistencies, boundary condition errors, and inefficient debugging loops. We conclude that, while current LLMs often demonstrate sufficient knowledge and intelligence to tackle space science tasks, they remain limited by an implementation barrier, functioning as powerful domain facilitators rather than fully autonomous engineers.