  Quantifying the level of atomic disorder within materials is critical to
understanding how evolving local structural environments dictate performance
and durability. Here, we leverage graph neural networks to define a physically
interpretable metric for local disorder. This metric encodes the diversity of
the local atomic configurations as a continuous spectrum between the solid and
liquid phases, quantified against a distribution of thermal perturbations. We
apply this novel methodology to three prototypical examples with varying levels
of disorder: (1) solid-liquid interfaces, (2) polycrystalline microstructures,
and (3) grain boundaries. Using elemental aluminum as a case study, we show how
our paradigm can track the spatio-temporal evolution of interfaces,
incorporating a mathematically defined description of the spatial boundary
between order and disorder. We further show how to extract physics-preserved
gradients from our continuous disorder fields, which may be used to understand
and predict materials performance and failure. Overall, our framework provides
an intuitive and generalizable pathway to quantify the relationship between
complex local atomic structure and coarse-grained materials phenomena.
