KappaFormer: Physics-aware Transformer for lattice thermal conductivity via cross-domain transfer learning

Machine learning has been widely used for predicting material properties. However, efficient prediction of lattice thermal conductivity ($\kappa_\mathrm{L}$) remains a long-standing challenge, primarily due to the scarcity of high-quality training data. Here we introduce KappaFormer, a physics-aware Transformer architecture that embeds the harmonic-anharmonic decomposition of $\kappa_\mathrm{L}$ within the network. KappaFormer comprises a harmonic branch pre-trained on large-scale elastic property data and an anharmonic branch fine-tuned on limited experimental $\kappa_\mathrm{L}$ data, enabling effective knowledge transfer and enhanced generalization. High-throughput screening with KappaFormer identifies multiple candidates with ultralow $\kappa_\mathrm{L}$, which are further confirmed by first-principles calculations. Physics interpretability further elucidates the vibrational mechanisms governing thermal transport suppression, linking structural motifs to strong anharmonicity. This study provides a generalizable framework for physics-guided machine learning to accelerate the discovery of new materials.