Fig. 1: The working framework of this study.

a 225 structural models were constructed by introducing 15 dopants and considered random arrangements of dopant atoms. Large-scale, high-throughput first-principles calculations were performed to obtain the energies of three phases for constructing the machine learning dataset. b Using Boltzmann distribution theory, we calculated the proportion of ferroelectric phases in HfO₂ thin films for different dopant types and doping concentrations, converting abstract energy differences into intuitive phase fraction distribution maps. c Descriptors were formed using weighted physical features, and feature space was expanded using the SISSO method. The dataset was divided into training and validation sets for machine learning model training. Model optimization was achieved through cross-validation and grid search for hyperparameter tuning, enabling large-scale predictions of dopants via machine learning. d With ferroelectric phase fraction and polarization value as the target properties, and guided by the predictions of the machine learning model, HfGaO ferroelectric thin films were successfully prepared in experiments. The variation patterns of ferroelectric properties and ferroelectric phases at different gallium doping concentrations were obtained, validating the reliability of the machine learning model.