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Optimizing a machine learning design of dielectric properties in lead-free piezoelectric ceramics

Designing lead-free piezoelectric ceramics with tailored electrical properties remains a critical challenge for various applications. In this paper we present a novel methodology integrating Machine Learning (ML) and optimization procedures to fine-tune electrical properties in lead-free (1-x) Na0.5 Bi0.5 TiO3 - x CaTiO3 piezoelectric ceramics. A comprehensive dataset of dielectric measurements serves as the foundation for training ML models that accurately predict the permittivity (𝜀′) and dielectric loss (tan 𝛿) as functions of Ca2+concentration (x % Ca), temperature and frequency. Two ML techniques are evaluated: random forest regression, and Multi-Layer Perceptron neural network Regression (MLPR). The MLPR model exhibited a superior regression performance, achieving a correlation coefficient of 0.931 and a root mean squared error of 0.029. The MLPR was then optimized by the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to maximizes 𝜀′ while minimizes tan 𝛿. Within the NSGA-II framework, the optimal values were found at the Pareto curve knee, corresponding to a frequency, temperature, and x % Ca of 609.739 kHz, 398.15 K, and 6.10, respectively, resulting in 𝜀′ equal to 857.87 and tan 𝛿 equal to 0.0120. This approach demonstrates the effectiveness of combining ML andoptimization for designing the electrical properties of piezoelectric ceramics, paving the way for more efficient and targeted material development.