Set-Based Training of Neural Barrier Certificates for Safety Verification of Dynamical Systems

• URL: http://arxiv.org/abs/2605.02526v1
• Date: Mon, 04 May 2026 12:27:20 GMT
• Title: Set-Based Training of Neural Barrier Certificates for Safety Verification of Dynamical Systems
• Abstract summary: Barrier certificates are functions that separate all unsafe states from all reachable states.<n>Recent approaches synthesize barrier certificates by iteratively training a neural network.<n>We propose a set-based training approach that tightly integrates verification into training.
• Score: 12.868690115701042
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Barrier certificates are scalar functions over the state space of dynamical systems that separate all unsafe states from all reachable states. The existence of a barrier certificate formally verifies the safety of the dynamical system. Recent approaches synthesize barrier certificates by iteratively training a neural network. In each iteration, the candidate is formally verified - if successful, the barrier certificate is found. Instead, we propose a set-based training approach that tightly integrates verification into training via a set-based loss function that soundly encodes all barrier certificate properties. A loss of zero formally proves the validity of the barrier certificate, collapsing the iterative training and verification into a single training procedure. Our experiments demonstrate that our set-based training approach scales well with the system dimension and naturally handles complex nonlinear dynamics.

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