  We show a data-driven approach to discover the underlying structural form of
the mathematical equation governing the dynamics of multiple but similar
systems induced by the same mechanisms. This approach hinges on theories that
we lay out involving arguments based on the nature of physical systems. In the
same vein, we also introduce a metric to search for the best candidate equation
using the datasets generated from the systems. This approach involves symbolic
regression by means of genetic programming and regressions to compute the
strength of the interplay between the extrinsic parameters in a candidate
equation. We relate these extrinsic parameters to the hidden properties of the
data-generating systems. The behavior of a new similar system can be predicted
easily by utilizing the discovered structural form of the general equation. As
illustrations, we apply the approach to identify candidate structural forms of
the underlying equation governing two cases: the changes in a sensor
measurement of degrading engines; and the search for the governing equation of
systems with known variations of an intrinsic parameter.
