from an integrated machine learning model*

Modeling the finite-temperature behavior of ferroelectric materials from first principles has always been challenging due to the large supercells and long simulation times required for adequate sampling.  Here we demonstrate the use of an integrated machine learning (ML) model of the potential energy and polarization surfaces of barium titanate (BaTiO₃) to overcome these difficulties and run long MD simulations with DFT accuracy. The integrated ML model allows us to study the microscopic nature of the paraelectric-ferroelectric transition and uncover surprising new insights, e.g. that the long-range, “needle-like” correlations observed previously can arise from a purely short-range model with no explicit long-range terms. Finally, we compute the frequency-dependent dielectric response function, finding a spectrum qualitatively similar that obtained with previous effective-Hamiltonian simulations as well as to experimentally measured profiles, with some remaining discrepancies that we trace back to the underlying DFT model. We expect this integrated, generally applicable modeling technique to become a valuable tool for elucidating the ferroelectric behavior of a wide variety of materials.