Can Deep Learning distinguish chaos from noise? Numerical experiments and general considerations

Within the larger field of real-world time series analysis, one of the most important tasks is the assessment of their stochastic vs. chaotic nature, and not surprisingly, many metrics and algorithms have been proposed to this end. A still under-explored option is offered by Deep Learning, i.e. a family of machine learning algorithms that perform automatic feature extraction and (usually supervised) classification. We here propose a series of numerical experiments aimed at assessing the performance of different Deep Learning models in discriminating between stochastic and chaotic time series generated by discrete maps, and at comparing such performance with that of standard metrics in the literature. Deep Learning clearly outperforms other alternatives, both in terms of minimum time series length and resilience to observational noise, and can be used to define a new gold standard against which old and new methods can be compared. At the same time, we explore more general considerations about the use of Deep Learning, including whether such models are able to detect general chaoticity fingerprints, or only patterns associated to specific chaotic maps; and what steps ought to be taken to make Deep Learning models a feasible instrument.