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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

Korean

Hamilton-Jacobi (HJ) 도달 가능성 분석은 제어 시스템에 대한 공식적인 안전 보증을 제공하지만 정확한 신경 인증서를 훈련하는 것은 특히 불안정한 영역을 특징화하기 어려울 때 어려울 수 있습니다. 우리는 이것을 검증 지시된 교육 프레임 워크를 사용하여 안전 제약의 확률적 인 계산을 해결합니다. 즉, 학습 된 인증서가 불안정한 행동을 잘못 분류하는 상태입니다. 이것은 표준 대립 공격 방법에 의해 생성 된 입력보다 실패 경계를 더 정확하게 캡처하는 컴팩트하고 타겟팅 된 대응 예제 세트를 생성합니다. 핵심적으로이 표현을 사용하여 미리 훈련 된 HJ 값 기능을 정의하여 더 큰 인증 영역을 생산하고 테스트 된 모든

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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