  The microscopic description of the local structure of water remains an open
challenge. Here, we adopt an agnostic approach to understanding water's
hydrogen bond network using data harvested from molecular dynamics simulations
of an empirical water model. A battery of state-of-the-art unsupervised
data-science techniques are used to characterize the free energy landscape of
water starting from encoding the water environment using local-atomic
descriptors, through dimensionality reduction and finally the use of advanced
clustering techniques. Analysis of the free energy at ambient conditions was
found to be consistent with a rough single basin and independent of the choice
of the water model. We find that the fluctuations of the water network occur in
a high-dimensional space which we characterize using a combination of both
atomic descriptors and chemical-intuition based coordinates. We demonstrate
that a combination of both types of variables are needed in order to adequately
capture the complexity of the fluctuations in the hydrogen bond network at
different length-scales both at room temperature and also close to the critical
point of water. Our results provide a general framework for examining
fluctuations in water under different conditions.
