Physics-Informed Surrogate Modelling of Finite-Size Scaling and Curie Temperature Suppression in Ferroelectric Perovskite Nanostructures

Finite-size suppression of the Curie temperature (T_c) in ferroelectric perovskite nanostructures remains an important yet insufficiently resolved problem, with reported scaling exponents varying considerably across experimental and theoretical studies. Although density functional theory provides atomistic insight into size-dependent behaviour, its high computational cost limits systematic exploration across broad size ranges. Conversely, purely empirical fitting approaches often lack physical interpretability and formal uncertainty quantification. In this work, a physics-informed surrogate modelling framework is developed to investigate finite-size scaling in BaTiO₃ and KNbO₃ nanostructures using a structured dataset compiled from the literature. The model is based on thermodynamically motivated scaling behaviour, enabling extraction of physically meaningful size-dependent parameters. Bootstrap resampling is employed to quantify statistical robustness, yielding scaling exponents of 1.59 (95% confidence interval: 1.43–1.72) for BaTiO₃ and 1.40 (95% confidence interval: 1.31–1.52) for KNbO₃. Gaussian Process regression is further integrated to provide uncertainty-aware predictions across the nanoscale domain. In addition to forward prediction, the framework enables inverse estimation of the minimum particle size required to preserve ferroelectric stability at a specified operating temperature. For a threshold of 300 K, the predicted critical sizes are approximately 4.96 nm for BaTiO₃ and 2.89 nm for KNbO₃. Extension to a coupled size–strain formulation produces a two-dimensional stability map, demonstrating tunable interactions between confinement and strain. Overall, the proposed methodology provides a transparent, statistically rigorous, and computationally efficient framework for predictive analysis and rational design of nanoscale ferroelectric materials.