Materials with perovskite phases are widely used in solar cells and ferroelectric, piezoelectric, dielectric and superconducting devices due to their various notable functions. However, structural instability limits some compositions in forming robust perovskite phases for device applications. The analytical approach using the tolerance factor (t) can only guarantee prediction accuracy within a limited range, ascribed to its nature of overlooking the atomic interaction. Hence, here we establish a prediction model using formation energy as the target parameter for its reflection of the reaction of atoms and apply machine learning as the analysis method since it has been successfully employed in plenty of material property prediction studies. Machine learning employs statistical methodologies to identify correlative patterns within large-scale datasets, enabling accurate predictions with robust generalization. In this work, we built a model to predict the formation energy of ABX₃ perovskite using machine learning and achieved a model with an R-squared value of 0.928 and a root mean square error of 0.301 eV/atom, validated by first-principles computations. In total, 75% of the values were correctly predicted within an error lower than 0.06. This work could contribute to accelerating the study of solving perovskites’ instability.

Addressing the requirements of advanced capacitor applications for high dielectric permittivity, low loss, and strong frequency stability necessitates the accelerated development of materials exhibiting weakly coupled relaxor ferroelectric characteristics and broad temperature stability. BaTiO3 systems have attracted considerable interest owing to their high dielectric constant and tunable properties. However, conventional trial-and-error approaches and complex doping strategies hinder rapid progress. In this study, a data-driven approach combining first-principles calculations with machine learning was employed to predict the variation trends in formation energies for 30 301 Sr, La co-doped BaTiO3 compositions. The ferroelectric properties, crystal structures, elastic anisotropy, and thermal properties were systematically investigated at four representative doping levels (0, 0.125, 0.25, and 0.375) to elucidate the microscopic mechanism responsible for the emergence of weakly coupled relaxor ferroelectric behavior and to enable rapid identification of doping ranges that yield both relaxor ferroelectric characteristics and broad temperature stability. The results show that Sr, La co-doping in the range of 0.125–0.25 introduces compositional and displacement disorder that progressively suppresses long-range ferroelectric order, promotes the formation of polar nanoregions, and drives the system toward a weakly coupled, relaxor-like dielectric response with reduced hysteretic loss, with the composition at 0.25 exhibiting enhanced mechanical and thermodynamic performance. These findings provide guidance for BaTiO3-based materials for high-frequency capacitor applications and offer a transferable framework for accelerating the study of doped material properties.