Standardized Non-Intrusive Reduced Order Modeling Using Different Regression Models With Application to Complex Flow Problems

arXiv (Cornell University)

Abstract

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.

Authors 4

1. Arturs Bērziņš Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Jan Helmig Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

3. Fabian Key

   TU Wien

   Affiliation as printed

   Vienna University of Technology

4. Stefanie Elgeti

   TU Wien

   Affiliation as printed

   Vienna University of Technology