# VIVALDy: AI-Driven Low-Order Modeling of Vortex-Induced Vibrations

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

► To cite this version:

Niccolò Tonioni, Lionel Agostini, Franck Kerhervé, Laurent Cordier, Ricardo Vinuesa. VIVALDy: AI-Driven Low-Order Modeling of Vortex-Induced Vibrations. Journée des doctorants, Jul 2025, Poitiers, France. [hal-05359032](https://hal.science/hal-05359032v1)

HAL Id: hal-05359032

https://hal.science/hal-05359032v1

Submitted on 11 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

Institut
Pprime

Recherche en physique
et ingénierie

<figure><img src="image_3.png" /></figure>

# VIVALDy: AI-Driven Low-Order Modeling of Vortex-Induced Vibrations

N.Tonioni*, L.Agostini*, F.Kerhervé*, L.Cordier*, R. Vinuesa^

* Curiosity Team, Pprime Institute, TSA 51124, Poitiers, FR

^ FLOW, Engineering Mechanics, KTH Royal Institute of Technology, SE-100 44, Stockholm, SE

## Introduction

**What is vortex induced vibration (VIV)?**

<figure><img src="image_4.png" /></figure>

**Fluid structure interaction:** Energy transfer from flow sustains structure motion that in turn directly influences shear layer dynamics.

<figure><img src="image_5.png" /></figure>

**Energy Harvesting:** Potential for harvesting clean energy from water currents.

**What is challenging?**

$A^*, U^*$

**Parameters Variability:** Model must generalize to "unseen" cases during training.

<figure><img src="image_6.png" /></figure>

**Minimal Observation:** Model input should solely be a minimal, easily accessible observation (e.g., cylinder displacement).

**What is the objective?**

**Efficient compact modeling of VIV:** a data-driven framework for turbulent flow around a one-degree of freedom oscillating cylinder, representative of VIV energy harvesting systems.

Experimental Set-up

<figure><img src="image_7.png" /></figure>

Dataset

<figure><img src="image_8.png" /></figure>

## Methods

<figure><img src="image_9.png" /></figure>

### Adversarial Loss

$$ \mathcal{L}_D = \mathbb{E}_{S \sim p_S}[-\log(1 - D(\tilde{S}))] + \mathbb{E}_{S \sim p_S}[-\log(D(S))] $$

$$ \mathcal{L}_{EG} = \mathbb{E}_{S \sim p_S}[d(S, \tilde{S}) + \beta D_{KL}(q_{W_E}(z|S) \| p_z) - \alpha \log(D(\tilde{S}))] $$

### How it works?

<figure><img src="image_10.png" /></figure>

**Training phase:** We first train two neural networks together: one that learns to compress flow patterns into key features (a β-VAE) and another that checks how realistic the generated flows are (discriminator). The two play an antagonistic game, one trying to deceive the other. Then, a transformer model is trained to predict how these key features evolve over time.

<figure><img src="image_11.png" /></figure>

**Inference phase:** After training, we only keep the transformer and the decoder. Given a new cylinder motion, they work together to reconstruct the full flow field—no need for the original encoder or discriminator anymore.

## Results

### Latent Variables

- Reveal quasi-periodic orbits ($\xi_2 - \xi_3$) linked to the two dominant vibration modes.

- Exhibit negative linear correlation indicating phase opposition ($\xi_1 - \xi_3$).

### Flow Reconstruction

- Accurately recovers dominant flow features with minimal error using only cylinder displacement.

### Learned Low-Dimensional Space

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

### Power Spectral Density at Sampling Point

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

## Conclusion

We introduced **Vivaldy**, an AI-based surrogate model for Vortex-Induced Vibration energy harvesting. It combines β-VAEs and GANs (Generative Adversarial Networks) to encode flow dynamics into a compact latent space, and uses a Transformer to predict it from cylinder motion alone. Results show accurate flow reconstructions and latent predictions from minimal input. Future work will explore using motion-based inference for **latent forecasting** and **data assimilation**.

CONTACT:
niccolo.tonioni@univ-poitiers.fr

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>