Atomistic simulations of nuclear fuel UO2 with machine learning interatomic potentials

We present the development of machine-learning interatomic potentials for uranium dioxide ${\mathrm{UO}}_{2}$. Density functional theory calculations with a Hubbard $U$ correction were leveraged to construct a training set of atomic configurations. This training set was designed to capture elastic and plastic deformations, as well as point and extended defects, and it was enriched through an active learning procedure. New configurations were added to the training database using a multiobjective criterion based on predicted uncertainties on energy and forces (obtained using a committee of models) and relative distances between new configurations in descriptor space. Two machine-learning potentials were developed based on physically sound pairwise potentials, which include the Coulombic interaction: a neural network potential and a SNAP potential. These potentials were optimized to minimize the root mean square error on the training database. Subsequently, the SNAP potential was used to compute the stacking fault energy surface in multiple directions, and the stabilized configurations were employed for subsequent DFT minimizations. The final DFT stacking fault energy surfaces of ${\mathrm{UO}}_{2}$ are presented, and the associated configurations are included in the training database for a new optimization. Finally, the results obtained from both machine-learned potentials were compared to standard semiempirical ones, demonstrating their excellent predictive capabilities for solid properties. These properties include defect formation energies, $\ensuremath{\gamma}$ surface, elastic properties, and phonon dispersion curves up to the Breidig transition temperature.