Machine learning-driven BaTiO ₃ -based high-entropy ceramics with ultrahigh energy storage density from crossover region

Abstract The high-entropy strategy has demonstrated significant advantages in improving the recoverable energy storage density (Wrec) and efficiency (η) of lead-free dielectric capacitors. However, exploring high-performance ceramics within the vast composition space of high-entropy systems using traditional trial-and-error methods remains highly challenging and inefficient. In this study, we employed a machine learning (ML)-accelerated strategy to overcome this limitation. A random forest regression model was developed using a dataset of BaTiO3 (BT)-based ceramics. Combined with the expected improvement acquisition function, this approach enabled efficient navigation through a space of 660,000 candidate compositions, markedly reducing the experimental burden compared with conventional methods. The optimal composition guided by ML, Ba0.24Sr0.24Bi0.26Na0.26Ti0.85Zr0.15O3, was experimentally verified to lie in the crossover region between relaxor ferroelectrics and superparaelectrics. In this region, the synergistic coexistence of nanodomains and polar nanoclusters leads to a large polarization difference between the maximum polarization and the remnant polarization (ΔP = Pmax − Pr), which is the structural origin of the ultrahigh Wrec of 10.8 J·cm−3 and high η of 86%. Furthermore, its excellent charge–discharge performance and stability in terms of temperature and frequency highlight its potential for practical applications, demonstrating the efficacy of machine learning in advancing energy storage ceramics.