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On the accuracy and efficiency of reduced order models: towards real-world applications

Pierfrancesco Siena, Paquale Claudio Africa, Michele Girfoglio, Gianluigi Rozza

Abstract

This chapter provides an extended overview about Reduced Order Models (ROMs), with a focus on their features in terms of efficiency and accuracy. In particular, the aim is to browse the more common ROM frameworks, considering both intrusive and data-driven approaches. We present the validation of such techniques against several test cases. The first one is an academic benchmark, the thermal block problem, where a Poisson equation is considered. Here a classic intrusive ROM framework based on a Galerkin projection scheme is employed. The second and third test cases come from real-world applications, the one related to the investigation of the blood flow patterns in a patient specific coronary arteries configuration where the Navier Stokes equations are addressed and the other one concerning the granulation process within pharmaceutical industry where a fluid-particle system is considered. Here we employ two data-driven ROM approaches showing a very relevant trade-off between accuracy and efficiency. In the last part of the contribution, two novel technological platforms, ARGOS and ATLAS, are presented. They are designed to provide a user-friendly access to data-driven models for real-time predictions for complex biomedical and industrial problems.

On the accuracy and efficiency of reduced order models: towards real-world applications

Abstract

This chapter provides an extended overview about Reduced Order Models (ROMs), with a focus on their features in terms of efficiency and accuracy. In particular, the aim is to browse the more common ROM frameworks, considering both intrusive and data-driven approaches. We present the validation of such techniques against several test cases. The first one is an academic benchmark, the thermal block problem, where a Poisson equation is considered. Here a classic intrusive ROM framework based on a Galerkin projection scheme is employed. The second and third test cases come from real-world applications, the one related to the investigation of the blood flow patterns in a patient specific coronary arteries configuration where the Navier Stokes equations are addressed and the other one concerning the granulation process within pharmaceutical industry where a fluid-particle system is considered. Here we employ two data-driven ROM approaches showing a very relevant trade-off between accuracy and efficiency. In the last part of the contribution, two novel technological platforms, ARGOS and ATLAS, are presented. They are designed to provide a user-friendly access to data-driven models for real-time predictions for complex biomedical and industrial problems.
Paper Structure (17 sections, 62 equations, 17 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 62 equations, 17 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Reduced order models
  3. Galerkin projection ROMs
  4. Data-driven ROMs
  5. Neural Networks
  6. Radial basis function
  7. Reduced basis generation
  8. Proper orthogonal decomposition
  9. Greedy algorithm
  10. Test cases
  11. Thermal block problem
  12. A cardiovascular application
  13. An industrial application
  14. Argos and Atlas
  15. Argos
  16. ...and 2 more sections

Figures (17)

  • Figure 1: Thermal block problem: computational domain.
  • Figure 2: Thermal block problem: error analysis for the temperature $u$ and the output of interest $s$ at varying of the number of basis functions.
  • Figure 3: Thermal block problem: qualitative comparison between FOM and ROM solution for the test point $\mu=(8,-1)$.
  • Figure 4: Cardiovascular benchmark. Sketch of the computational domain: Coronary Artery Bypass Graft (CABG) with Left Internal Thoracic Artery (LITA), Left Main Coronary Artery (LMCA), Left Anterior Descending Artery (LAD) and Left Circumflex artery (LCx) (left panel). Inflow boundary conditions imposed on LITA and LMCA sections (right panel).
  • Figure 5: Cardiovascular benchmark: introduction of stenosis in the LMCA using FFD technique.
  • ...and 12 more figures