2020/06/24 by Arturs Bērziņš, Bērziņš, Artūrs, Jan Helmig +5 · 1 citation
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Hydraulic and Pneumatic Systems #Model Reduction and Neural Networks #Nuclear Engineering Thermal-Hydraulics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2006.13706
openalex publication_date 2020/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.