Parametric model order reduction techniques often struggle to accurately represent transport-dominated phenomena due to a slowly decaying Kolmogorov n-width. To address this challenge, we propose a non-intrusive, data-driven methodology that combines the shifted proper orthogonal decomposition (POD) with deep learning. Specifically, the shifted POD technique is utilized to derive a high-fidelity, low-dimensional model of the flow, which is subsequently utilized as input to a deep learning framework to forecast the flow dynamics under various temporal and parameter conditions. The efficacy of the proposed approach is demonstrated through the analysis of one- and two-dimensional wildland fire models with varying reaction rates, and its performance is evaluated using multiple error measures. The results indicate that the proposed approach yields highly accurate results within the percent range, while also enabling rapid prediction of system states within seconds.

翻译：参数化模型降阶技术在处理传输主导现象时，常因科尔莫戈罗夫n-宽度衰减缓慢而难以准确表征。针对这一挑战，我们提出一种非侵入式、数据驱动的方法，将移位本征正交分解（POD）与深度学习相结合。具体而言，利用移位POD技术推导出高保真、低维的流动模型，随后将其作为深度学习框架的输入，以预测不同时间和参数条件下的流动动态。通过分析具有不同反应速率的一维和二维野火模型验证了所提方法的有效性，并采用多种误差测度评估其性能。结果表明，该方法在百分比范围内可获得高精度结果，同时能够在数秒内快速预测系统状态。