Learning Spatio-Temporal Specifications for Dynamical Systems
This work addresses the challenge of understanding and controlling dynamical systems with time-varying spatial patterns, but it appears incremental as it extends existing Signal Temporal Logic.
The authors tackled the problem of learning formal logic specifications for dynamical systems from data, proposing SVM-STL to specify spatio-temporal properties and demonstrating it on a reaction-diffusion system example.
Learning dynamical systems properties from data provides important insights that help us understand such systems and mitigate undesired outcomes. In this work, we propose a framework for learning spatio-temporal (ST) properties as formal logic specifications from data. We introduce SVM-STL, an extension of Signal Signal Temporal Logic (STL), capable of specifying spatial and temporal properties of a wide range of dynamical systems that exhibit time-varying spatial patterns. Our framework utilizes machine learning techniques to learn SVM-STL specifications from system executions given by sequences of spatial patterns. We present methods to deal with both labeled and unlabeled data. In addition, given system requirements in the form of SVM-STL specifications, we provide an approach for parameter synthesis to find parameters that maximize the satisfaction of such specifications. Our learning framework and parameter synthesis approach are showcased in an example of a reaction-diffusion system.