Decoupled geometry–physics learning for volumetric defect-density reconstruction in pulsed infrared thermography

Pulsed infrared thermography enables non-contact subsurface-defect evaluation, but reconstructing internal volumetric defect-density fields from surface thermal sequences remains an ill-posed heat-diffusion inverse problem. Preserving sharp topology while enforcing smooth diffusion-consistent thermal evolution can create competing optimization demands. We propose the Decoupled Geometry–Physics Network (DGPN) to address this tension through a geometry-first sequence. Stage 1 learns a supervised geometry prior, Stage 2 adds normalized local diffusion-consistency regularization, and geometry-anchored test-time optimization (TTO) optionally refines a sample-specific latent variable with network parameters fixed. Controlled synthetic experiments show a statistically supported within-DGPN gain from Stage 1 to Stage 2 and support input-conditioned reconstruction. In the primary comparison on real polyvinyl chloride (PVC) data, Stage 1, trained without synthetic-domain pretraining, achieves the highest feed-forward layer-macro mean proxy Dice (0.8757) among the evaluated complete configurations. TTO recovers 0.0118 Dice from Stage 2 and attains the highest layer-macro mean proxy Dice and intersection over union (IoU) in this comparison (0.8787 and 0.7885). Its small 0.0030 difference from Stage 1 is not statistically significant, supporting complementary feed-forward and offline-refinement modes. Because each real target repeats a computer-aided design (CAD)-assisted mask across ten output layers, these scores quantify proxy-label agreement, not independently measured internal geometry. Ablation results support geometry anchoring over unanchored refinement. Within this scope, DGPN provides a strong real-only feed-forward reconstruction route and an optional geometry-anchored offline refinement for data-limited thermographic inspection.