Data-Driven or Model-Constrained? Comparing Airflow Estimation Methods under Sparse Sensing

Airflow-driven advection is the primary mechanism for gas and aerosol dispersion in real-world scenarios, making accurate airflow estimation essential for ventilation monitoring, gas source localization, and contaminant spread analysis. Since obtaining airflow maps via high-resolution spatial sensing is usually infeasible in practice, flow field estimation methods must cope with sparse measurements by introducing statistical or physical priors to compensate for limited data. Existing approaches mainly differ in how they incorporate fluid-flow constraints and environmental geometry. However, due to the lack of systematic comparisons across this spectrum of methods, the potential benefits of physics-based priors for airflow estimation under sparse sensing remain underexplored. To address this question, we quantitatively evaluate four airflow estimators across three simulated 2D scenarios under steady-state conditions and varying sampling densities. The methods range from Gaussian Process Regression and graph-based Gaussian Markov Random Fields to two Navier-Stokes-based approaches, including a novel strong-form residual minimization variant. Our results show that physical priors provide the greatest benefit at low sampling densities by compensating for missing spatial information. Although data-driven Gaussian Process Regression becomes increasingly competitive as sensor coverage increases, model-based estimators retain an accuracy advantage across the evaluated scenarios.