Physics-Informed Graph Diffusion Model for Cross-Scale Performance Prediction of Silver Nanowire Percolation Networks

Silver nanowire (AgNW) networks are promising transparent conductive electrodes (TCEs) for flexible optoelectronics, yet their industrial quality control is hindered by the gap between invisible microstructures and unpredictable macroscopic performance. Herein, we propose a Physics-informed Graph Diffusion Model that injects the physical laws governing TCE conduction into deep learning as an inductive bias. From a single scanning electron micrograph, we construct a topology graph and predict the sheet resistance, Rs. A physics-informed GIN encoder, pretrained on a resistor-network-derived conductance label, provides a robust cold-start representation; a target-posterior diffusion model then supplies a calibrated per-prediction uncertainty rather than performing latent manifold augmentation. The encoder is trained on a multisource graph data set that fuses synthetic percolation models with real SEM micrographs of AgNW films at three sheet-resistance levels, augmented by an external continuous-Rs data set. Under a leakage-free, group-aware evaluation, the two-stage model predicts Rs with a relative error of 7.27% (R² = 0.840) while delivering calibrated uncertainty (empirical 1σ/2σ coverage of 63.6%/92.4% versus the nominal 68.3%/95.4%). Film-scale-level validation across the three held-out film-scale groups (the held-out in-house film at both fields of view plus one held-out external film) gives 6.21% ± 4.66% (mean ± std), and a stricter leave-one-film-out protocol over the three in-house films gives a 5.51% mean (4.75/7.72/4.06%). The diffusion module's distinctive contribution is calibrated uncertainty quantification; its point accuracy is statistically indistinguishable from a no-diffusion baseline. Requiring only 108k parameters and trained on 13 source SEM images, the model matches strong graph baselines while uniquely supplying calibrated prediction intervals for industrial TCE inspection.