  Machine-learned interatomic potentials enable realistic finite temperature
calculations of complex materials properties with first-principles accuracy. It
is not yet clear, however, how accurately they describe anharmonic properties,
which are crucial for predicting the lattice thermal conductivity and phase
transitions in solids and, thus, shape their technological applications. Here
we employ a recently developed on-the-fly learning technique based on molecular
dynamics and Bayesian inference in order to generate an interatomic potential
capable to describe the thermodynamic properties of zirconia, an important
transition metal oxide. This machine-learned potential accurately captures the
temperature-induced phase transitions below the melting point. We further
showcase the predictive power of the potential by calculating the heat
transport on the basis of Green-Kubo theory, which allows to account for
anharmonic effects to all orders. This study indicates that machine-learned
potentials trained on the fly offer a routine solution for accurate and
efficient simulations of the thermodynamic properties of a vast class of
anharmonic materials.
