  The presence of a second critical point in water has been a topic of intense
investigation for the last few decades. The molecular origins underlying this
phenomenon are typically rationalized in terms of the competition between local
high-density (HD) and low-density (LD) structures. Their identification often
require designing parameters that are subject to human intervention. Herein, we
use unsupervised learning to discover structures in atomistic simulations of
water close to the Liquid-Liquid Critical point (LLCP). Encoding the
information of the environment using local descriptors, we do not find evidence
for two distinct thermodynamic structures. In contrast, when we deploy
non-local descriptors that probe instead heterogeneities on the nanometer
length scale, this leads to the emergence of LD and HD domains rationalizing
the microscopic origins of the density fluctuations close to criticality.
