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Parametric model order reduction techniques often struggle to accuratelyrepresent transport-dominated phenomena due to a slowly decaying Kolmogorovn-width. To address this challenge, we propose a non-intrusive, data-drivenmethodology that combines the shifted proper orthogonal decomposition (POD)with deep learning. Specifically, the shifted POD technique is utilized toderive a high-fidelity, low-dimensional model of the flow, which issubsequently utilized as input to a deep learning framework to forecast theflow dynamics under various temporal and parameter conditions. The efficacy ofthe proposed approach is demonstrated through the analysis of one- andtwo-dimensional wildland fire models with varying reaction rates, and itsperformance is evaluated using multiple error measures. The results indicatethat the proposed approach yields highly accurate results within the percentrange, while also enabling rapid prediction of system states within seconds.

Parametric model order reduction for a wildland fire model via the shifted POD based deep learning method