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Data repairing and resolution enhancement using data-driven modal decomposition and deep learning

A. Hetherington, D. Serfaty, A. Corrochano, J. Soria, S. Le Clainche

TL;DR

The paper tackles the challenge of incomplete, noisy, and under-resolved fluid-dynamics data from experiments and simulations. It presents a data-driven framework that couples modal decomposition (SVD/POD and high-order SVD) with deep learning to repair data and upscale resolution. Key contributions include gappy SVD/HOSVD for missing data repair, an SVD superresolution algorithm, and a hybrid DL superresolution model with hyperparameter tuning plus uncertainty quantification, demonstrated on three complex test cases. The results show robust data repair, effective resolution enhancement, and noise filtering, highlighting practical benefits for reducing computational costs and enabling large-scale data-driven analyses, with the tools made available in ModelFLOWs-app.

Abstract

This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase the quality and precision of numerical and experimental data. A combination of two- and three-dimensional, numerical and experimental dasasets are used to demonstrate the reconstruction capacity of the presented methods, showing that these methods can be used to reconstruct any type of dataset, showing outstanding results when applied to highly complex data, which is noisy. The combination of benefits of these techniques results in a series of data-driven methods which are capable of repairing and/or enhancing the resolution of a dataset by identifying the underlying physics that define the data, which is incomplete or under-resolved, filtering any existing noise. These methods and the Python codes are included in the first release of ModelFLOWs-app.

Data repairing and resolution enhancement using data-driven modal decomposition and deep learning

TL;DR

The paper tackles the challenge of incomplete, noisy, and under-resolved fluid-dynamics data from experiments and simulations. It presents a data-driven framework that couples modal decomposition (SVD/POD and high-order SVD) with deep learning to repair data and upscale resolution. Key contributions include gappy SVD/HOSVD for missing data repair, an SVD superresolution algorithm, and a hybrid DL superresolution model with hyperparameter tuning plus uncertainty quantification, demonstrated on three complex test cases. The results show robust data repair, effective resolution enhancement, and noise filtering, highlighting practical benefits for reducing computational costs and enabling large-scale data-driven analyses, with the tools made available in ModelFLOWs-app.

Abstract

This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase the quality and precision of numerical and experimental data. A combination of two- and three-dimensional, numerical and experimental dasasets are used to demonstrate the reconstruction capacity of the presented methods, showing that these methods can be used to reconstruct any type of dataset, showing outstanding results when applied to highly complex data, which is noisy. The combination of benefits of these techniques results in a series of data-driven methods which are capable of repairing and/or enhancing the resolution of a dataset by identifying the underlying physics that define the data, which is incomplete or under-resolved, filtering any existing noise. These methods and the Python codes are included in the first release of ModelFLOWs-app.
Paper Structure (18 sections, 14 equations, 21 figures, 4 tables)

This paper contains 18 sections, 14 equations, 21 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Data reparation and resolution enhancement based on modal decomposition methods and deep learning
  3. Data organization
  4. Singular value decomposition
  5. Gappy SVD and gappy HOSVD
  6. SVD superresolution algorithm
  7. Deep learning superresolution (DL superresolution)
  8. Error analysis using uncertainty quantification
  9. Test cases
  10. Three-dimensional circular cylinder
  11. Turbulent circular cylinder
  12. Rough flat plate turbulent boundary layer
  13. Results
  14. Data repairing with gappy SVD
  15. Data resolution enhancement applying the SVD superresolution algorithm
  16. ...and 3 more sections

Figures (21)

  • Figure 1: Gappy SVD: sketch summarizing the methodology.
  • Figure 2: SVD superresolution algorithm: sketch summarizing the methodology.
  • Figure 3: Reconstruction of databases combining SVD and deep learning architectures. Sketch of the methodology.
  • Figure 4: Sketch with the training, validation and test set distribution for the deep learning module.
  • Figure 5: Streamwise (left), normal (middle) and spanwise (right) velocities of a representative snapshot of the three-dimensional cylinder dataset at Re $= 280$ from VegaLeClaincheBook20.
  • ...and 16 more figures