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 R2 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.