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A data-driven framework for spatial-temporal prediction is proposed forreducing the computational cost of industrial thermal striping applications.The framework aims to efficiently identify the flow features and utilize themin spatiotemporal field predictions with a limited number of full-ordersimulations. In a parameterized system, the classical projection-basedsurrogates often suffer from Kolmogorov n-width limitations and have limitedreducibility in highly-nonlinear systems. A two-level machine learningframework is proposed based on physics to address this issue. The selection ofmachine learning algorithms and information extraction is empowered by the ideathat the thermal striping phenomenon is driven by large turbulent coherent flowstructures. In the first level, the turbulence coherent structures areidentified and collected by performing Proper Orthogonal Decomposition on localparameters. A tree-based machine-learning model is then used to down-select thereference structures based on the physical meaning of the modes. In the secondlevel, the reference structure information is broken down into pointwise localpoints for training a deep structure corrector, which corrects the bias betweenthe locally true and reference structures. Demonstration of a selectedindustrial application, triple jet, shows that the method can capture thefluctuation frequencies and amplitudes of the spatiotemporal fields in a highlynonlinear setting. The result shows that the prediction root-mean-squared errorof velocity is 0.031 for all 3,844 spatial points.

Development of a Two-Level ML Spatial-temporal Framework for Industrial Thermal Striping Applications