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

2026-02-11

AI Summary

This work addresses the challenge of verifying closed-loop safety in safety-critical systems—such as aerospace applications—where neural network controllers act as black boxes. The authors propose a sampling-free reachability analysis framework that embeds a trained neural network into the system dynamics to form an autonomous closed-loop system. By integrating high-order Taylor expansions, automated domain partitioning, and polynomial bounding techniques, the method rigorously confines the propagation of state uncertainties over event manifolds. This approach enables, for the first time, a global, sound, and efficient reachability analysis of neural network-controlled systems, yielding tight upper and lower bounds on controller outputs across large state spaces. These guaranteed bounds facilitate reliable safety certification and informed mission-level decision-making.

Technology Category

• Natural Language Processing: Safety and Robustness
• Multiagent Systems: Multiagent Systems under Uncertainty
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• neural network controllers
• safety assessment
• sample-free verification
• black-box systems
• spaceflight applications

Innovation

• Taylor methods
• neural network verification
• polynomial bounding
• automatic domain splitting
• safety assessment