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\% for the predicted velocity, pressure and temperature distributions. We find that GPR can offer several advantages over an ANN, constituting a viable and computationally inexpensive non-intrusive RBM .
In recent years, numerical methods in industrial applications have evolved from a pure predictive tool towards a means for optimization and control. Since standard numerical analysis methods have become prohibitively costly in such multi-query settings, a variety of reduced order modeling (ROM) approaches have been advanced towards complex applications. In this context, the driving application for this work is twin-screw extruders (TSEs): manufacturing devices with an important economic role in plastics processing. Modeling the flow through a TSE requires non-linear material models and coupling with the heat equation alongside intricate mesh deformations, which is a comparatively complex scenario. We investigate how a non-intrusive, data-driven ROM can be constructed for this application. We focus on the well-established proper orthogonal decomposition (POD) with regression albeit we introduce two adaptations: standardizing both the data and the error measures as well as -- inspired by our space-time simulations -- treating time as a discrete coordinate rather than a continuous parameter. We show that these steps make the POD-regression framework more interpretable, computationally efficient, and problem-independent. We proceed to compare the performance of three different regression models : Radial basis function (RBF) regression, Gaussian process regression (GPR) , and artificial neural networks (ANNs). We find that GPR offers several advantages over an ANN, constituting a viable and computationally inexpensive non-intrusive ROM. Additionally, the framework is open-sourced to serve as a starting point for other practitioners and facilitate the use of ROM in general engineering workflows .
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In recent years, numerical methods in industrial applications have evolved from a pure predictive tool towards a means for optimization and control. Since standard numerical analysis methods have become prohibitively costly in such multi-query settings, a variety of reduced order modeling (ROM) approaches have been advanced towards complex applications. In this context, the driving application for this work is twin-screw extruders (TSEs): manufacturing devices with an important economic role in plastics processing. Modeling the flow through a TSE requires
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material models and coupling with the heat equation alongside intricate mesh deformations, which is a comparatively complex scenario. We investigate how a non-intrusive, data-driven ROM can be constructed for this application. We focus on the well-established
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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\% for the predicted velocity, pressure and temperature distributions.
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