Uncertainty-aware reduced-order modelling with sparse sensing and data assimilation for forecasting combustion dynamics

Abstract Accurate and efficient prediction of combustion dynamics remains challenging due to the nonlinear and multiscale nature of reactive flows. High-fidelity simulations are often impractical for real-time applications due to their computational cost. Reduced-order models offer a promising alternative but their predictive capability may decay when the operating conditions differ from those represented in the training data. This work develops an uncertainty-aware reduced-order modelling framework for combustion dynamics, combining Multi-scale Proper Orthogonal Decomposition (mPOD), Gaussian Process Regression (GPR), sparse sensing and data assimilation. The latent dynamics extracted by mPOD is learned offline using GPR, while sparse sensing is employed during the forecast to enable data assimilation in the latent space from limited observations. The frequency organization introduced by mPOD and the characteristics temporal scales identified in the latent dynamics are used to define the temporal covariance structure of the GPR. Different GPR kernel formulations, spatial sensing constraints, latent-state reconstruction methods, and assimilation frequencies are systematically assessed. The approach is evaluated on two different datasets: an experimental dataset comprising chemiluminescence images from a forced swirled turbulent flame, and a numerical dataset of an axi-symmetric, time-varying, non-premixed laminar flame. The results show that a Periodic GPR kernel provides the most robust latent forecast across both datasets, while regularized least squares and Bayesian sparse reconstruction methods improve robustness under limited spatial accessibility. Data assimilation further compensates for forecast deviations by combining noisy sparse observations with the probabilistic GPR forecast. In the laminar-flame case, six temperature measurements are sufficient to substantially enhance an inaccurate Cosine GPR kernel forecast and achieve prediction errors approaching those obtained with the best-performing Periodic kernel. These results demonstrates the potential of the proposal framework for uncertainty-aware forecasting of combustion dynamics by combining probabilistic reduced-order modelling, sparse observations and data assimilation.