Microstructure-Mediated Inverse Design of Thermal Barrier Coatings via Interpretable, Data-Efficient Machine Learning

Microstructure control is critical for thermal barrier coating (TBC) performance, yet the complex, nonlinear process-structure relationships impede predictive design. Conventional data-driven approaches are limited by scarce experimental data and poor physical interpretability in end-to-end models. Here, we present a closed-loop machine learning framework that decouples the process-property relationship by introducing microstructure as a physically interpretable intermediary, thereby enabling accurate optimization with only 45 training samples and 3 validation experiments. Key microstructure features such as equiaxed pores, unmelted regions, and cracks are quantitatively identified from scanning electron microscopy images using a deep neural network-based image recognition module, enabling automated feature extraction for subsequent modeling and optimization. The resulting forward prediction models achieve <i>R</i>² values of 0.896, 0.878, and 0.727 for equiaxed pores, unmelted regions, and cracks, respectively. These models further uncover dominant mechanisms, including current-distance interactions that govern thermal energy distribution and gas flow-feed rate coupling that influence particle trajectory. The inverse design engine converts target microstructures into manufacturing parameters with 92% structural reproduction accuracy and 88% parameter prediction accuracy. Experimental validation confirms that coatings designed for low thermal conductivity achieve 35-46% reductions at 1000 °C relative to the data set average, realized with only two fabrication iterations. By explicitly decomposing the process-property relationship into interpretable process-structure and structure-property links, this framework shifts TBC development from empirical iteration into data-efficient, intelligent precision design and offers a generalizable strategy for interpretable materials design under data scarcity.