  Phase diagrams are an invaluable tool for material synthesis and provide
information on the phases of the material at any given thermodynamic condition.
Conventional phase diagram generation involves experimentation to provide an
initial estimate of thermodynamically accessible phases, followed by use of
phenomenological models to interpolate between the available experimental data
points and extrapolate to inaccessible regions. Such an approach, combined with
first-principles calculations and data-mining techniques, has led to exhaustive
thermodynamic databases albeit at distinct thermodynamic equilibria. In
contrast, materials during their synthesis, operation, or processing, may not
reach their thermodynamic equilibrium state but, instead, remain trapped in a
local free energy minimum, that may exhibit desirable properties. Mapping these
metastable phases and their thermodynamic behavior is highly desirable but
currently lacking. Here, we introduce an automated workflow that integrates
first principles physics and atomistic simulations with machine learning (ML),
and high-performance computing to allow rapid exploration of the metastable
phases of a given elemental composition. Using a representative material,
carbon, with a vast number of metastable phases without parent in equilibrium,
we demonstrate automatic mapping of hundreds of metastable states ranging from
near equilibrium to those far-from-equilibrium. Moreover, we incorporate the
free energy calculations into a neural-network-based learning of the equations
of state that allows for construction of metastable phase diagrams. High
temperature high pressure experiments using a diamond anvil cell on graphite
sample coupled with high-resolution transmission electron microscopy are used
to validate our metastable phase predictions. Our introduced approach is
general and broadly applicable to single and multi-component systems.
