Physics-Informed Neural Operators for Generalizable and Label-Free Inference of Temperature-Dependent Thermoelectric Properties

Accurate characterization of temperature-dependent thermoelectric properties (TEPs), such as thermal conductivity and the Seebeck coefficient, is essential for reliable modeling and efficient design of thermoelectric devices. However, their nonlinear temperature dependence and coupled transport behavior make both forward simulation and inverse identification difficult, particularly under sparse measurement conditions. In this study, we develop a physics-informed machine learning approach that employs physics-informed neural networks (PINN) for solving forward and inverse problems in thermoelectric systems, and neural operators (PINO) to enable generalization across diverse material systems. The PINN enables field reconstruction and material property inference by embedding governing transport equations into the loss function, while the PINO generalizes this inference capability across diverse materials without retraining. Trained on simulated data for 20 p-type materials and evaluated on 60 unseen materials, the PINO model demonstrates accurate and label-free inference of TEPs using only sparse field data. The proposed framework offers a scalable, generalizable, and data-efficient approach for thermoelectric property identification, paving the way for high-throughput screening and inverse design of advanced thermoelectric materials.