Data-Driven Compositional Safety Verification of Interconnected Monotone Systems

Abstract

This paper introduces a sample-efficient compositional method for formal safety verification of interconnected monotone systems without requiring explicit models of the local subsystems. Existing data-driven approaches either lack formal safety guarantees or rely on dense Lipschitz-based discretizations of the state space to provide such guarantees, which leads to significant computational overhead and limits scalability. In contrast, we leverage the monotonicity of local subsystems to construct tractable local interval-barrier certificates using only boundary evaluations of each subsystem in a decentralized manner, together with a global condition that guarantees the safety of the overall interconnected system. At the local level, our framework learns interval-barrier certificates using monotone neural networks from boundary samples induced by partitions of the local state and internal-input spaces. At the global level, it composes these local neural interval-barrier certificates using the interconnection structure to certify the safety of the overall system. Furthermore, under appropriate structural assumptions, we reformulate the global safety condition into a scalable form that can be directly incorporated into the neural network loss. This enables the enforcement of overall system safety during local training. The experimental results demonstrate the effectiveness and scalability of the proposed method.