Scalable safety verification with simultaneous accuracy and efficiency for high-dimensional systems

Develop safety verification techniques for high-dimensional dynamical systems that simultaneously achieve rigorous accuracy and computational efficiency, overcoming the curse of dimensionality that affects Hamilton–Jacobi reachability and mixed-integer programming-based verification approaches.

Background

The paper notes that gold-standard verification tools such as Hamilton–Jacobi reachability and MILP-based verification suffer from severe scalability issues, limiting their applicability to real-world, high-dimensional systems.

Although decomposition methods and neural approximations have been explored, the challenge remains to ensure both tight, reliable guarantees and computational efficiency in a unified, scalable framework.

References

Although decomposition techniques and neural approximations have been proposed, ensuring both accuracy and efficiency remains a critical open problem.

— Safe Physics-Informed Machine Learning for Dynamics and Control  (2504.12952 - Drgona et al., 17 Apr 2025) in Section 6: Challenges and Opportunities

While some are accurate and all have polynomial-time complexity, it is not clear that they are fast or simple enough for time-domain distance protection.

— Reachability-based Time-domain Distance Protection  (2608.19678 - Taylor et al., 20 Aug 2026) in Section 3, Fault tests, immediately preceding Section 4

Control barrier functions and reachability analysis can define safe sets for low-level control, though scaling them to perception-conditioned, multi-agent, high-dimensional E2E policies remains difficult.

— Planning-Oriented End-to-End Autonomous Driving: Architectures, Evaluation, and Emerging Paradigms  (2608.20111 - Guan et al., 20 Aug 2026) in Section 6.3, Runtime Assurance and Safety Envelopes