Enumeration-Guided Training of Neural Hamilton-Jacobi Safety Certificates

Mihaela-Larisa Clement, Tosca Pierro, Ezio Bartocci, Luca Marzari · 2026 · arXiv

DOI: 10.48550/arXiv.2610.27870 · open-access PDF

Abstract

Hamilton-Jacobi (HJ) reachability analysis offers formal safety guarantees for control systems, but training accurate neural certificates remains difficult, particularly when unsafe regions are hard to characterize. We propose a verification-guided training framework that addresses this by using probabilistic enumeration of safety constraints to detect forward-invariance violations, i.e., states where the learned certificate incorrectly classifies unsafe behavior. This produces a compact, targeted set of counterexamples that more precisely captures the failure boundary than inputs generated by

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