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Divergence detection and flow structure analysis in POD-DL predictions of a hydrogen-methane flame

par Zou, Xiangrui;Parente, Alessandro ;Le Clainche, Soledad
Référence European journal of mechanics. B, Fluids, 119, 204515
Publication Publié, 2026-07-01

Article révisé par les pairs

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Résumé :

Predictive simulations are essential for flow control and combustion applications, where fast and computationally efficient methods are required. Reduced order models (ROMs) combined with deep learning (DL) offer a promising solution by compressing high-dimensional flow data which retaining key physical features. However, their predictive reliability deteriorates when applied to scenarios beyond the training range. Detecting divergence in such surrogate models is therefore critical, especially in the absence of ground truth, or in real time deployment where on-the-fly retraining may be necessary. In this study, we propose and compare several approaches to evaluate the divergence of the predicted results. First, a hybrid framework combining proper orthogonal decomposition and deep learning (POD-DL) is employed to forecast the temporal evolution of flame in a canonical jet-in-hot-coflow burner based on large eddy simulation (LES) data. Reasonable agreement is achieved by comparing the distributions of temperature and representative species, and analyzing relative root mean square error (RRMSE) between LES and predicted results. Secondly, to monitor reliability without ground truth, three divergence detection strategies are investigated: (1) prediction using different retained POD modes, (2) different random seeds, and (3) Mahalanobis distance analysis in POD coefficient space. The first two methods use relative spatial mean and L 2-norm errors for assessing, while the Mahalanobis-distance approach quantifies statistical deviation from the training manifold. Finally, POD spatial modes are examined for various predicted cases, and the comparison between the normalized singular values reveals that the predictions begin to diverge from the LES data around snapshot 300–350. All methods consistently detect the onset of divergence around snapshot 300–350, aligning with the RRMSE trend, with the Mahalanobis-based method demonstrating superior sensitivity and robustness. These findings provide a framework for dynamic uncertainty estimation and adaptive prediction in data-driven flow modeling.