Learning Spatio-Temporal Specifications for Dynamical Systems

Learning dynamical systems properties from data provides valuable insights that help us understand such systems and mitigate undesired outcomes. We propose a framework for learning spatio-temporal (ST) properties as formal logic specifications from data. We introduce Support-Vector Machine-Signal Temporal Logic (SVM-STL), an extension of Signal Temporal Logic (STL), capable of specifying spatial and temporal properties of a wide range of systems exhibiting 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.