Scenario Approach and Conformal Prediction for Verification of Unknown Systems via Data-Driven Abstractions

Rudi Coppola, Andrea Peruffo, Lars Lindemann, Manuel Mazo Jr.

Abstract: Verification of uncertain, complex dynamical systems is crucial in the modern day world. An increasingly common method to verify complex logic specifications for dynamical systems involves symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. By sampling trajectories of the concrete, unknown system and via robust analysis, we build a data-driven abstraction, related to the underlying model through a probabilistic behavioural inclusion relation. As the distribution from which the trajectories are drawn is unknown, we adopt two distinct distribution-free theories, namely scenario optimization and conformal prediction. We compare and discuss the differences between the two approaches in terms of the type of guarantees that they are able to provide. Furthermore, via experimental benchmarks we outline the efficiency of the two methods with respect to the number of samples available and the tightness of the guarantees.