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

TL;DR

This paper introduces a physics-informed scenario approach for safety verification of nonlinear systems, reducing data requirements by selecting samples based on physics-based models and observed data alignment.

Contribution

It proposes a novel data selection method that integrates physics models with data to improve safety verification efficiency for nonlinear systems.

Findings

Reduces data requirements for safety verification.

Successfully applied to three case studies.

Guides scenario optimization with physics-informed data selection.

Abstract

This paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs) to ensure that system trajectories remain within safe regions over an infinite time horizon. Designing BCs often relies on an accurate dynamics model; however, such models are often imprecise due to the model complexity involved, particularly when dealing with highly nonlinear systems. In such cases, while scenario approaches effectively address the safety problem using collected data to construct a guaranteed BC for the unknown dynamical system, they often require solving an optimization problem with substantial amounts of data. To address this, we propose a physics-informed scenario approach that selects data samples such that the outputs of the physics-based model and the observed data are sufficiently close. This approach guides the scenario optimization process to eliminate redundant samples and potentially reduce the required dataset size. We validate our approach through three case studies, showcasing its practical application in reducing the required data.