  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.
