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 modeling and design of thermoelectric devices. However, nonlinear temperature dependence and coupled transport behavior make forward simulation and inverse identification challenging under sparse measurements. We present a physics-informed machine learning framework combining physics-informed neural networks (PINN) and neural operators (PINO) for solving forward and inverse problems in thermoelectric systems. PINN enables field reconstruction and property inference by embedding governing equations into the loss function, while PINO generalizes across materials without retraining. Trained on simulated data for 20 p-type materials and tested on 60 unseen materials, PINO accurately infers TEPs using only sparse temperature and voltage data. This framework provides a scalable, data-efficient, and generalizable solution for thermoelectric property identification, facilitating high-throughput screening and inverse design of advanced thermoelectric materials.