  The identification of self-similarity is an indispensable tool for
understanding and modelling physical phenomena. Unfortunately, this is not
always possible to perform formally in highly complex problems. We propose a
methodology to extract the similarity variables of a self-similar physical
process directly from data, without prior knowledge of the governing equations
or boundary conditions, based on an optimization problem and symbolic
regression. We analyze the accuracy and robustness of our method in four
problems which have been influential in fluid mechanics research: a laminar
boundary layer, Burger's equation, a turbulent wake, and a collapsing cavity.
Our analysis considers datasets acquired via both numerical and wind-tunnel
experiments.
