Physics-Informed Neural Network for Sparse-Sensor Inverse Heat Conduction

This study develops a sparse-sensor physics-informed neural network (PINN) to reconstruct a transient two-dimensional thermalfield and identify thermal diffusivity, volumetric heat loss, and source amplitude from noisy point measurements. Sixteen interiorsensors provide 5424 observations for a moving-source benchmark. The nominal model achieves a mean root-mean-square error(RMSE) of 3.52 × 10−3 normalized temperature units and a global relative L2 error of 2.87 × 10−2. The corresponding relativeerrors in the three identified coefficients are 5.04%, 24.54%, and 7.90%. Under matched data, architecture, initialization, anditeration budget, the physics-informed model reduces mean RMSE by 96.03% relative to a conventional data-only neural networkand by 95.56% relative to spatiotemporal interpolation. One-factor-at-a-time tests indicate that spatial sensor scarcity and lossweighting are more influential than temporal subsampling over the ranges examined. The results show that governing-equationconstraints provide strong regularization for sparse thermal reconstruction; however, the sensitivity results are diagnostic ratherthan statistical, and experimental validation remains necessary before deployment