Learning Spatio-Temporal Specifications for Dynamical Systems

TL;DR

This paper introduces SVM-STL, a machine learning framework for deriving spatio-temporal logic specifications from data of dynamical systems, enabling better understanding and control of complex spatial-temporal behaviors.

Contribution

The paper presents SVM-STL, an extension of STL for spatio-temporal properties, and develops methods for learning these specifications from data and synthesizing parameters to satisfy them.

Findings

Successfully learned spatio-temporal specifications from system data.

Demonstrated the framework on a reaction-diffusion system example.

Provided methods for both labeled and unlabeled data scenarios.

Abstract

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.