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VIVALDy: A Hybrid Generative Reduced-Order Model for Turbulent Flows, Applied to Vortex-Induced Vibrations

Niccolò Tonioni, Lionel Agostini, Franck Kerhervé, Laurent Cordier, Ricardo Vinuesa

Abstract

Developing reduced-order models applicable to fluid-dynamics problems involving complex geometries and different flow conditions remains a critical challenge for turbulent flows. This study introduces VIVALDy, a novel machine-learning framework that employs a hybrid $β$-Variational Autoencoder-Generative Adversarial Network ($β$-VAE-GAN) architecture with masked convolutions to extract dominant flow features into a compact latent space while preserving fidelity at solid-fluid interfaces. A bidirectional transformer then models the temporal evolution of these features, learning to predict flow trajectories from minimal sensor inputs. This two-stage approach enables the transformer to map sensor measurements to dominant flow variables identified by the autoencoder, advancing reduced-order modeling capabilities for real-time flow prediction. The effectiveness of the framework is demonstrated through application to a problem relevant to vortex-induced vibration (VIV) energy harvesting systems, reconstructing the turbulent flow around a one-degree-of-freedom moving cylinder. Validated against experimental data spanning fluid-structure interaction regimes of interest, VIVALDy accurately predicts different flow states using only the cylinder displacement. The framework demonstrates adequate performance in both reconstruction accuracy and statistical fidelity across diverse operating conditions, enabling efficient prediction of the turbulent flow phenomena governing vortex-induced vibration.

VIVALDy: A Hybrid Generative Reduced-Order Model for Turbulent Flows, Applied to Vortex-Induced Vibrations

Abstract

Developing reduced-order models applicable to fluid-dynamics problems involving complex geometries and different flow conditions remains a critical challenge for turbulent flows. This study introduces VIVALDy, a novel machine-learning framework that employs a hybrid -Variational Autoencoder-Generative Adversarial Network (-VAE-GAN) architecture with masked convolutions to extract dominant flow features into a compact latent space while preserving fidelity at solid-fluid interfaces. A bidirectional transformer then models the temporal evolution of these features, learning to predict flow trajectories from minimal sensor inputs. This two-stage approach enables the transformer to map sensor measurements to dominant flow variables identified by the autoencoder, advancing reduced-order modeling capabilities for real-time flow prediction. The effectiveness of the framework is demonstrated through application to a problem relevant to vortex-induced vibration (VIV) energy harvesting systems, reconstructing the turbulent flow around a one-degree-of-freedom moving cylinder. Validated against experimental data spanning fluid-structure interaction regimes of interest, VIVALDy accurately predicts different flow states using only the cylinder displacement. The framework demonstrates adequate performance in both reconstruction accuracy and statistical fidelity across diverse operating conditions, enabling efficient prediction of the turbulent flow phenomena governing vortex-induced vibration.

Paper Structure

This paper contains 26 sections, 14 equations, 14 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Dataset Generation and Preparation
  3. Experimental Setup and Data Acquisition
  4. Preparation of 2D Flow Snapshots for Model Input
  5. VIVALDy: A Machine-Learning Framework for Data-Driven Flow Modeling
  6. Masked Convolutions for Solid-Fluid Interface Fidelity
  7. Latent-Feature Extraction using a $\beta$-VAE-GAN Architecture
  8. Latent-Space Dynamics from Cylinder Kinematics using a Bidirectional Transformer
  9. Models Training Details
  10. Results
  11. Ablation Study on Adversarial Loss Term
  12. Evaluation metrics
  13. Results analysis
  14. Latent-Space Trajectory Prediction
  15. Methodological Framework
  16. ...and 11 more sections

Figures (14)

  • Figure 1: Schematic representation of VIVALDy framework. Training phase: The $\beta$-variational autoencoder ($\beta$-VAE) and discriminator are trained simultaneously in a generative adversarial framework, where the decoder serves as generator and receives evaluative feedback from the discriminator. A transformer model is then trained to predict latent variable evolution using only cylinder displacement $y_{\mathrm{cyl}}$ as input. Inference phase: Only the transformer and decoder are retained to generate flow field predictions from displacement signals.
  • Figure 2:
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  • ...and 9 more figures