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Machine-learned interatomic potentials enable realistic finite temperaturecalculations of complex materials properties with first-principles accuracy. Itis not yet clear, however, how accurately they describe anharmonic properties,which are crucial for predicting the lattice thermal conductivity and phasetransitions in solids and, thus, shape their technological applications. Herewe employ a recently developed on-the-fly learning technique based on moleculardynamics and Bayesian inference in order to generate an interatomic potentialcapable to describe the thermodynamic properties of zirconia, an importanttransition metal oxide. This machine-learned potential accurately captures thetemperature-induced phase transitions below the melting point. We furthershowcase the predictive power of the potential by calculating the heattransport on the basis of Green-Kubo theory, which allows to account foranharmonic effects to all orders. This study indicates that machine-learnedpotentials trained on the fly offer a routine solution for accurate andefficient simulations of the thermodynamic properties of a vast class ofanharmonic materials.

Thermal transport and phase transitions of zirconia by on-the-fly machine-learned interatomic potentials