Physics-enhanced residual learning framework for high-fidelity reconstruction from sparse data

Reconstructing high-fidelity physical fields from sparse measurements is a critical challenge in engineering and physics. Traditional data-driven methods, such as Proper Orthogonal Decomposition (POD) and deep learning, struggle with extrapolation and often inherit systematic biases from simulation data. Meanwhile, Physics-Informed Neural Networks (PINNs) frequently face convergence difficulties and spurious solutions when measurements are sparse and boundary conditions are incomplete. To address these limitations, a physics-enhanced residual learning framework is proposed. This approach reformulates the sparse reconstruction task as a base data correction problem. First, a stable low-fidelity base field is obtained via POD. Subsequently, a PINN is employed to learn the nonlinear residuals relative to this base field, constrained by data supervision, governing equations, and prior physical knowledge. This framework combines the computational efficiency of reduced-order modeling with the generalization capability of physics-constrained learning. Reconstruction results of the turbine vane temperature field indicate that, compared to traditional POD, the proposed method reduces reconstruction relative L 2 error from 2.69% to 1.02% under extrapolated boundary condition and exhibits improved tolerance to sensor noise. Under actual experimental conditions, the average relative L 2 error across 18 conditions is lowered from 1.55% to 0.42%, effectively correcting inherent biases between simulation-based results and experiments. Furthermore, the relative L 2 error using only 17 sensors (0.57%) surpasses that of POD using 45 sensors (1.16%), demonstrating high data efficiency and potential for engineering deployment. This study provides a general algorithmic formulation and demonstrates its effectiveness for high-fidelity temperature field reconstruction in a cooled turbine vane.