On data-driven identification: Is automatically discovering equations of motion from data a Chimera?

In this paper, a simple inverted pendulum is considered in order to discover, or extract, its dynamic equation from experimental data acquired during proper motion. This textbook case study achieved both in numerical simulations and with an off-the-shelf hardware reveals structural deficiencies in algorithms pretending to distill physics from data. In short, the outcome is that the obtained equations are not reliable and thus the model is practically equivalent to a black-box one. The data appropriateness is checked against a model-based identification. Is automatically discovering equations of motion from data then a Chimera?