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

The methods that this review discusses aspire to address one or more of these concerns, with overcoming the computational bottlenecks being the main research achievement and dealing with the hard epistemic barriers remaining a yet unresolved research challenge.

— Engineering safe structures: recent advances in structural reliability modelling  (2609.26440 - Sharma et al., 22 Sep 2026) in Section 5.3, Discussion on particle and trajectory splitting methods; Section 9.0, Closure and suggested future directions