Sparse-Sensor PINN Reconstruction and Identification

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

This paper studies a sparse-sensor physics-informed neural network (PINN) for reconstructing a transient

two-dimensional thermal field and jointly identifying thermal parameters from pointwise noisy observations.

The benchmark problem is a square plate governed by a heat equation with linear volumetric loss, homogeneous

Dirichlet boundaries, a moving localized heat source, and a weaker secondary hot spot. Only sixteen

randomly distributed interior sensors with additive Gaussian noise are used to inform the inverse model.

The proposed formulation combines data-fidelity, PDE-residual, boundary-condition, initial-condition,

and parameter-prior losses, while positivity of the unknown coefficients is enforced through exponential

reparameterization. Numerical simulations are carried out, and the corresponding reconstruction and

parameter-identification results are presented and discussed.