From the harmonic phonons of ZrO 2 in Fig. , we observe that cubic zirconia is predicted to be dynamically unstable with an imaginary phonon mode at the X-point of the Brillouin zone. The eigenvector of this mode corresponds to a distortion to the tetragonal phase with a doubling of the unit cell. This distortion from the cubic phase is favourable in terms of internal energy. Thus, to understand the observed dynamic stability of this polymorph, we must resort to an anharmonic description, which we perform within the framework of self-consistent phonon (SCPH) theory . The anharmonic force constants are determined using compressive sensing (see Methods for details), which allows for extraction of highorder force constants at a significantly lower computational cost compared with direct determination of the force constants using symmetry-adapted finite displacements .