Standardized Non-Intrusive Reduced Order Modeling Using Different Regression Models With Application to Complex Flow Problems
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We present a non-intrusive reduced basis method (RBM) for unsteady non-linear parametrized partial differential equations (PDEs) based on proper orthogonal decomposition (POD) with regression. Three different regression models are compared, including radial basis function (RBF) regression, Gaussian process regression (GPR) and artificial neural networks (ANNs). The established method is extended with additional preprocessing steps, including centering before POD, standardization by singular values before regression and a standardized error measure. These steps benefit the interpretability and allow to reuse the presented framework on different problems. Furthermore, we propose to treat time not as a parameter but rather as a discretized coordinate similar to space. The approach is first validated on steady as well as time-dependent driven cavity viscous flows. Additionally, we study the flow of plastic melt inside across-section of a co-rotating twin-screw extruder. This is characterized by a time- and temperature-dependent flowof a generalized Newtonian fluid on a moving domain. The achieved standardized errors are less than 3 find that GPR can offer several advantages over an ANN, constituting a viable and computationally inexpensive non-intrusive RBM.
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