  We demonstrate the possibility of classifying causal systems into kinds that
share a common structure without first constructing an explicit dynamical model
or using prior knowledge of the system dynamics. The algorithmic ability to
determine whether arbitrary systems are governed by causal relations of the
same form offers significant practical applications in the development and
validation of dynamical models. It is also of theoretical interest as an
essential stage in the scientific inference of laws from empirical data. The
algorithm presented is based on the dynamical symmetry approach to dynamical
kinds. A dynamical symmetry with respect to time is an intervention on one or
more variables of a system that commutes with the time evolution of the system.
A dynamical kind is a class of systems sharing a set of dynamical symmetries.
The algorithm presented classifies deterministic, time-dependent causal systems
by directly comparing their exhibited symmetries. Using simulated, noisy data
from a variety of nonlinear systems, we show that this algorithm correctly
sorts systems into dynamical kinds. It is robust under significant sampling
error, is immune to violations of normality in sampling error, and fails
gracefully with increasing dynamical similarity. The algorithm we demonstrate
is the first to address this aspect of automated scientific discovery.
