Physics-informed diffusion models for 3D reconstruction of indoor gaseous pollutant fields from sparse measurements

Indoor gaseous pollutant concentration fields are essential to evaluating ventilation effectiveness and occupant exposure, yet their spatial distribution is highly heterogeneous due to transient sources and recirculating flows. Sparse and noisy sensor networks make it difficult to reconstruct a continuous, physically consistent three-dimensional (3D) field. To address this issue, a physics-informed diffusion model with an enhanced RIME optimization framework (IRIME-PIDM) is proposed for 3D gaseous pollutant reconstruction from sparse observations. First, by integrating detrending, normalization, and random Fourier feature embedding, the generative diffusion model is effectively applied to environmental field reconstruction. The proposed preprocessing techniques and signal-to-noise (SNR)-weighted loss function stabilize learning across diffusion steps, resulting in smooth and high-fidelity reconstruction of synthetic data, with an R² of 0.922, MAE of 48.2 ppm, and RMSE of 61.3 ppm. Second, a steady-state convection-diffusion-reaction (CDR) constraint is incorporated as a physical regularization term to ensure that the reconstructed field satisfies conservation laws and exhibits realistic transport behavior. On real-world measurements, PIDM achieves an R² of 0.848, MAE of 11.49 ppm, and RMSE of 16.23 ppm, significantly outperforming the ANN and XGBoost baselines. Third, the IRIME algorithm adaptively adjusts diffusion steps, learning rate, and network width through temperature-style scheduling and adhesion control, enhancing convergence robustness. Compared to rime optimization algorithm (RIME), the R² increases by 4.5%, while the MAE and RMSE decrease by 12.5% and 24.7%, respectively. This study presents a deployable, physically consistent 3D gaseous pollutant sensing solution for intelligent buildings, facilitating healthy ventilation, demand-controlled ventilation, and exposure assessment.