Decoding the multi-scale physical origins of rare-earth-doped PMN-PT with large piezoelectric coefficient by interpretable machine learning

High-performance lead-based relaxor-ferroelectric Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 (PMN-PT) piezoceramics constitute a critical class of functional materials for advanced electromechanical transduction. However, achieving further performance enhancement is fundamentally hindered by the complexity of compositional optimization, particularly the choice of rare-earth dopant species and their precise concentrations. Machine learning (ML) has emerged as a transformative tool for navigating these high-dimensional compositional spaces and decoding complex physical origins. Herein, an interpretable and uncertainty-informed ML framework is developed to systematically investigate the piezoelectric coefficient ( d 33 ) of rare-earth-doped PMN-PT ceramics. By integrating ensemble regression with a multidimensional interpretability scheme, the framework explicitly decodes the underlying physical mechanisms, identifying the key factors governing d 33 variation, including rare-earth concentration, local structural disorder, B-site electronegativity, and lattice geometry. Guided by these insights, Sm and Eu are identified as the most promising dopants, with the highest predicted d 33 occurring near 2.5 mol% substitution. Predictive uncertainty remains well-controlled within the high-performance compositional domain near the morphotropic phase boundary (MPB), where the localized variance reflects the intrinsic structural instability and strong phase competition. This work establishes an interpretable and reliability-aware framework for deciphering complex solid solutions, bridging the gap between atomic-scale descriptors and macroscopic electromechanical properties.