Physics-Prior and Multi-Scale Attention-Based Three-Dimensional Quality Field Reconstruction for Sparse Industrial Manufacturing Inspection

INTRODUCTION: Three-dimensional quality field reconstruction from sparse industrial measurements is critical for intelligent manufacturing yet remains challenging due to sensor accessibility limitations, high inspection costs, and component occlusion. OBJECTIVES: This study develops a reconstruction framework that recovers full-domain three-dimensional fields from sparse observations by integrating physics-based constraints with data-driven deep learning, and validates it on simulated three-dimensional optical scattering fields that serve as a controlled, physically rigorous proxy for industrial quality fields. METHODS: A physics-guided loss function embedding Helmholtz equation residuals and boundary conditions is constructed, combined with a multi-scale three-dimensional convolutional network incorporating serial channel-spatial attention to capture both global structural and local high-frequency defect features. The benchmark fields are solved on a 128 × 128 × 128 grid, and 5% of voxels are retained as labeled samples. RESULTS: Under 5% sparse sampling of the simulated optical scattering fields, the proposed framework achieved the best reconstruction performance among all compared methods. On 40 independent test samples, it reached a PSNR of 34.6 ± 1.3 dB, an SSIM of 0.932 ± 0.011, and a phase RMSE of 0.183 ± 0.025 rad, outperforming MS-CNN by 4.5 dB, 0.049, and 33.2%, respectively. Visual comparisons showed improved recovery of strong scattering regions, boundary variations, diffraction-focus positions, and high-frequency defect-related structures, with an average peak-intensity error of about 4.2% and centroid deviation of about 0.3 μm. Under noisy inputs, the method retained PSNR above 29 dB and SSIM above 0.88 at SNR = 10 dB, indicating stronger robustness than 3D U-Net and standard PINN. Ablation experiments (reported as mean ± standard deviation over the 40 test fields) further confirmed that physical constraints, multi-scale convolution, channel attention, and spatial attention each contributed to the overall performance gain, with paired statistical tests confirming significant improvements across the main comparisons. CONCLUSION: The framework offers a robust, physically consistent route for sparse quality-field reconstruction in intelligent manufacturing. Validation currently relies on high-fidelity numerical simulation; extension to real industrial measurements is identified as the primary direction of future work.