  In this paper we develop the stability rules for NASICON structured
materials, as an example of compounds with complex bond topology and
composition. By applying machine learning to the ab-initio computed phase
stability of 3881 potential NASICONs we can extract a simple two-dimensional
descriptor that is extremely good at separating stable from unstable NASICONS.
This machine-learned "tolerance factor" contains information on the Na content,
the radii and electronegativities of the elements, and the Madelung energy. We
test the predictive capability of this approach by selecting six predicted
NASICON compositions. Five out of the six resulted in a phase pure NASICON
while the sixth composition led to a NASICON that coexisted with other phases,
validating the efficacy of this approach. This work not only provide tools to
understand synthetic accessibility of NASICON-type materials, but also
demonstrate an efficient paradigm for discovering new materials with complicate
composition and atomic structure.
