# Research on Enumeration-Guided Training of Neural Hamilton-Jacobi Safety Certificates

- Source: arXiv cs.RO
- Published: 2026-10-21T04:00:00.000Z
- RoboHot: https://robohot.news/en/items/jgen04k8osvpib5ft3dt1nvtb
- Original: https://arxiv.org/abs/2610.27870

## Summary

This research proposes a verification-guided training framework that uses probabilistic enumeration of safety constraints to detect forward-invariance violations, generating counterexample sets that are more compact and closer to the failure boundary than those from standard adversarial attack methods. Fine-tuning a pretrained HJ value function with these counterexamples expands the certifiable region and shortens certification time across all tested benchmarks; the authors also introduce a deployment-time shielding mechanism based on the refined certificates, achieving zero safety constraint violations in Isaac Sim physics simulation and real-world autonomous racing experiments compared with a nominal controller and an LQR-based backup strategy.