Physics-Informed Safety Verification of Nonlinear Systems: A Scenario Approach with Data Mitigation

Designing barrier certificates (BCs) to ensure system safety often relies on an accurate dynamical model. In such cases, while scenario approaches effectively address the safety problem using collected data to construct a guaranteed BC for dynamical systems with unknown mathematical models, they often require substantial amounts of data---sometimes millions of samples---due to exponential sample complexity. To mitigate the required number of data, we propose a physics-informed scenario approach that selects data samples such that the outputs of the (imprecise) physics-based model and the observed data are sufficiently close (within a specified threshold). This approach guides the scenario optimization process to eliminate redundant samples and significantly reduce the required dataset size. We demonstrate the capability of our approach in mitigating the amount of data required for scenario optimizations while providing correctness guarantees.