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Enumeration-Guided Training of Neural Hamilton-Jacobi Safety Certificates

Mihaela-Larisa Clement, Tosca Pierro, Ezio Bartocci, Luca Marzari · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27870 · cited by 0 works (OpenAlex) · open-access PDF

Indonesian

Analisis aksesibilitas Hamilton-Jacobi (HJ) menawarkan jaminan keamanan formal untuk sistem kontrol, tetapi pelatihan sertifikat saraf yang akurat tetap sulit, terutama ketika wilayah yang tidak aman sulit didefinisikan. Kami mengusulkan kerangka kerja pelatihan yang dipandu oleh verifikasi yang menangani hal ini dengan menggunakan daftar probabilis dari keterbatasan keamanan standar untuk mendeteksi pelanggaran-invariance ke depan, yaitu, keadaan di mana sertifikat yang dipelajari secara tidak benar mengklasifikasikan perilaku yang tidak aman. Ini menghasilkan serangkaian kontrasepsi yang kompak dan ditargetkan yang lebih akurat menangkap batas kegagalan daripada input yang dihasilkan oleh metode serangan lawan standar. Yang penting, menggunakan representasi ini untuk menyesuaikan fungsi HJ yang diprediksi menghasilkan wilayah yang disertifikasi yang lebih besar dan mengurangi waktu sertifikasi di seluruh benchmark yang diuji

Machine translation (Meta M2M100); the English original follows.

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 standard adversarial attack methods. Crucially, using this representation to fine-tune a pretrained HJ value function yields larger certified regions and reduces certification time across all tested benchmarks. We further introduce a shielding mechanism based on the refined certificates to enforce safety constraints at deployment time. We evaluate the proposed safety filter in a realistic, physics-based Isaac Sim environment and through real-world autonomous racing experiments, achieving zero safety constraint violations compared to a nominal controller and a backup policy based on Linear Quadratic Regulation (LQR). These results demonstrate the effectiveness of the proposed shielding mechanism in ensuring safe operation under high-speed, safety-critical conditions.

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Topics: Computer science, Certification, Probabilistic logic, Backup, Certificate, System safety

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