  Vibrational properties of solids are key to determining stability, response
and functionality. However, they are challenging to computationally predict at
Ab-Initio accuracy, even for elemental systems. Ab-Initio methods for modeling
atomic interactions are limited in the system sizes and simulation times that
can be achieved. Due to these limitations, Machine Learning Interatomic
Potentials (MLIPs) are gaining popularity and success as a faster, more
scalable approach for modeling atomic interactions, potentially at Ab-Initio
accuracy. Even with faster potentials, methodologies for predicting entropy,
free energy and vibrational properties vary in accuracy, cost and difficulty to
implement. Using the Covariance of Atomic Displacements (CAD) to predict
entropy, free energy and finite-temperature phonon dispersions is a promising
approach but thorough benchmarking has been hampered by the cost of Ab-Initio
methods for sampling. In this work, we use a MLIP and the CAD to characterize
the convergence of the predicted properties and determine optimal sampling
strategies. We focus on solid lithium at zero pressure, showing that the
MLIP-CAD approach reproduces experimental entropy, phonon dispersions and the
martensitic transition while also comparing to more established methods.
