Environment-adaptive machine-learned force fields for materials under extreme conditions: hafnium and hafnium dioxide polymorphs

Advances in machine-learned interatomic potentials have enabled the prediction of complex material properties with accuracy approaching that of ab initio methods. However, it is unclear how the finite capacity of such models affects their ability to achieve consistent accuracy across diverse thermodynamic conditions without introducing trade-offs. In this paper, we present two computationally efficient interatomic potentials capable of accurately simulating the behavior of hafnium and hafnium dioxide across a very wide variety of thermodynamic conditions. Our approach combines Latin Hypercube and Monte Carlo Sampling for generating diverse data sets, with an extended formulation of the recently-developed environment-adaptive proper orthogonal descriptors. Molecular dynamics simulations show that the resulting potentials accurately reproduce density functional theory results and experimental data for pressure- and temperature-induced phase transitions as well as other properties associated with the materials’ polymorphs and liquid phases. We further showcase the versatility of the environment-adaptive formulation by using our potential to compute the shock Hugoniot of hafnium up to temperatures and pressures of 1 MK and 1 TPa, respectively; good agreement with available experimental data is observed.