  A data-driven framework for spatial-temporal prediction is proposed for
reducing the computational cost of industrial thermal striping applications.
The framework aims to efficiently identify the flow features and utilize them
in spatiotemporal field predictions with a limited number of full-order
simulations. In a parameterized system, the classical projection-based
surrogates often suffer from Kolmogorov n-width limitations and have limited
reducibility in highly-nonlinear systems. A two-level machine learning
framework is proposed based on physics to address this issue. The selection of
machine learning algorithms and information extraction is empowered by the idea
that the thermal striping phenomenon is driven by large turbulent coherent flow
structures. In the first level, the turbulence coherent structures are
identified and collected by performing Proper Orthogonal Decomposition on local
parameters. A tree-based machine-learning model is then used to down-select the
reference structures based on the physical meaning of the modes. In the second
level, the reference structure information is broken down into pointwise local
points for training a deep structure corrector, which corrects the bias between
the locally true and reference structures. Demonstration of a selected
industrial application, triple jet, shows that the method can capture the
fluctuation frequencies and amplitudes of the spatiotemporal fields in a highly
nonlinear setting. The result shows that the prediction root-mean-squared error
of velocity is 0.031 for all 3,844 spatial points.
