Sparse-Sensor PINN Reconstruction and Identification

This studies a sparse-sensor PINN for reconstructing a transient thermal field and jointly identifying thermal parameters

This study develops a sparse-sensor physics-informed neural network (PINN) to reconstruct a transient

two-dimensional thermal field and identify thermal diffusivity, volumetric heat loss, and source amplitude

from noisy point measurements. Sixteen interior sensors 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 relative errors in the

three identified coefficients are 5.04%, 24.54%, and 7.90%. Under matched data, architecture, initialization,

and iteration budget, the physics-informed model reduces mean RMSE by 96.03% relative to a conventional

data-only neural network and by 95.56% relative to spatiotemporal interpolation. One-factor-at-a-time tests

indicate that spatial sensor scarcity and loss weighting are more influential than temporal subsampling over

the ranges examined. The results show that governing-equation constraints provide strong regularization

for sparse thermal reconstruction; however, the sensitivity results are diagnostic rather than statistical, and

experimental validation remains necessary before deployment.