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Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation

Anna Ivagnes, Nicola Demo, Gianluigi Rozza

TL;DR

This work tackles expensive CFD inverse problems by introducing a non-intrusive ROM workflow that fuses three ANN roles: boundary parametrization to generate injector-like wake inputs, dimensionality reduction via POD or Autoencoder to compress full-field data, and parametric solution-manifold approximation via RBF or ANN to predict wake fields for new parameters. The pipeline is optimized end-to-end with a Genetic Algorithm, enabling robust global search in the reduced space. Two CFD test cases on Navier–Stokes flow in a circular cylinder demonstrate the method: a smooth wake distribution and a sparse set of wake observations, with results showing that POD-ANN and linear AE-ANN can perform strongly under limited data, while nonlinear AE variants require regularization to avoid overfitting. Overall, the framework provides a flexible, data-driven template for rapid boundary inference in inverse problems, with potential for real-time or many-query applications in engineering settings.

Abstract

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the iterative optimization process. To accelerate such a procedure, we apply a numerical pipeline that involves artificial neural networks to parametrize the boundary conditions of the problem in hand, compress the dimensionality of the (full-order) snapshots, and approximate the parametric solution manifold. It derives a general framework capable to provide an ad-hoc parametrization of the inlet boundary and quickly converges to the optimal solution thanks to model order reduction. We present in this contribution the results obtained by applying such methods to two different CFD test cases.

Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation

TL;DR

This work tackles expensive CFD inverse problems by introducing a non-intrusive ROM workflow that fuses three ANN roles: boundary parametrization to generate injector-like wake inputs, dimensionality reduction via POD or Autoencoder to compress full-field data, and parametric solution-manifold approximation via RBF or ANN to predict wake fields for new parameters. The pipeline is optimized end-to-end with a Genetic Algorithm, enabling robust global search in the reduced space. Two CFD test cases on Navier–Stokes flow in a circular cylinder demonstrate the method: a smooth wake distribution and a sparse set of wake observations, with results showing that POD-ANN and linear AE-ANN can perform strongly under limited data, while nonlinear AE variants require regularization to avoid overfitting. Overall, the framework provides a flexible, data-driven template for rapid boundary inference in inverse problems, with potential for real-time or many-query applications in engineering settings.

Abstract

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the iterative optimization process. To accelerate such a procedure, we apply a numerical pipeline that involves artificial neural networks to parametrize the boundary conditions of the problem in hand, compress the dimensionality of the (full-order) snapshots, and approximate the parametric solution manifold. It derives a general framework capable to provide an ad-hoc parametrization of the inlet boundary and quickly converges to the optimal solution thanks to model order reduction. We present in this contribution the results obtained by applying such methods to two different CFD test cases.
Paper Structure (22 sections, 23 equations, 13 figures, 7 tables)

This paper contains 22 sections, 23 equations, 13 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Boundary parametrization using ANN
  4. Model Order Reduction
  5. Dimensionality reduction
  6. Proper Orthogonal Decomposition
  7. Autoencoder
  8. Approximation techniques
  9. Radial Basis Functions
  10. Artificial Neural Networks
  11. Wake optimization
  12. Numerical results
  13. The inverse problem
  14. First test case: a smooth distribution
  15. Parametrization using $\text{ANN}$
  16. ...and 7 more sections

Figures (13)

  • Figure 1: Flow diagram for the data-driven pipeline followed in the paper.
  • Figure 2: Schematic structure of an autoencoder.
  • Figure 3: Representation of the mesh on a slice orthogonal to the cylinder axis (left), and on the walls (right).
  • Figure 4: The computational domain.
  • Figure 5: Structure of the $\text{ANN}$ used for parametrization.
  • ...and 8 more figures