Title: Do Machine-Learning Atomic Descriptors and Order Parameters Tell the Same Story? The Case of Liquid Water

Abstract: Machine-learning (ML) has become a key workhorse in molecular simulations. Building an ML model in this context, involves encoding the information of chemical environments using local atomic descriptors. In this work, we focus on the Smooth Overlap of Atomic Positions (SOAP) and their application in studying the properties of liquid water both in the bulk and at the hydrophobic air-water interface. By using a statistical test aimed at assessing the relative information content of different distance measures defined on the same data space, we investigate if these descriptors provide the same information as some of the common order parameters that are used to characterize local water structure such as hydrogen bonding, density or tetrahedrality to name a few. Our analysis suggests that the ML description and the standard order parameters of local water structure are not equivalent. In particular, a combination of these order parameters probing local water environments can predict SOAP similarity only approximately, and viceversa, the environments that are similar according to SOAP are not necessarily similar according to the standard order parameters. We also elucidate the role of some of the metaparameters entering in the SOAP definition in encoding chemical information.