Real-Time Indoor CO₂ Distribution Prediction Using CFD and Physics Regularized Kolmogorov-Arnold Network

Bert S Turner Department of Construction Management, Louisiana State University, Baton Rouge, LA 70803, USA

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract

Carbon dioxide (CO₂) is widely used as a practical indicator of indoor air quality and ventilation performance, yet its indoor distribution is often spatially non-uniform because of room geometry, airflow structure, ventilation configuration, and occupant-generated emissions. This study proposes a hybrid CFD-AI framework that integrates baseline computational fluid dynamics (CFD) with sparse sensor measurements through a physics-regularized Kolmogorov-Arnold Network (KAN) to reconstruct high-resolution indoor CO₂ fields. The framework was demonstrated in a mechanically ventilated university classroom instrumented with five NDIR CO₂ sensors and synchronized HVAC data. A steady Reynolds-averaged Navier-Stokes CFD model with SST k-ω turbulence closure and passive-scalar CO₂ transport was used to generate baseline concentration and airflow fields, which were interpolated to sensor locations to define residual targets. The KAN was trained using spatial coordinates, time encodings, HVAC variables, and CFD priors within a composite loss function that combined data fidelity, physics residuals, and spatiotemporal smoothness constraints. Leave-one-sensor-out validation showed strong generalization to unseen sensor locations, reducing MAE from 123.09 to 28.00 ppm and RMSE from 123.39 to 29.20 ppm, corresponding to error reductions of approximately 65-92% across folds. The corrected fields also preserved spatial coherence in breathing-zone CO2 contours. These results demonstrate that physics-regularized residual learning can substantially improve sensor-sparse indoor CO2 mapping and support room-scale ventilation assessment and control.