VIVALDy Reconstruction
Ground Truth
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 its application to a problem relevant to vortex-induced vibration (VIV) energy harvesting systems, reconstructing 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, demonstrating robust performance in both reconstruction accuracy and statistical fidelity across diverse operating conditions.
The VIVALDy framework combines two complementary architectures: a hybrid β-VAE-GAN to extract dominant flow features into a compact latent space, and a bidirectional transformer to map sensor measurements to the flow variables identified by this latent space. Masked convolutions are employed within the CNN architectures in the encoder and discriminator to handle solid structures in the convolution field of view, significantly improving solid-fluid interface reconstruction quality. The use of the hybrid architecture allows combining the individual strengths of both models, resulting in improved distribution-preserving properties compared to a standard VAE and a more structured, informative latent space than that offered by a standalone GAN.
Training Phase: The β-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 variables evolution using only cylinder displacement as input.
Inference Phase: Only the transformer and decoder are retained to generate flow field predictions from displacement signals, enabling real-time flow reconstruction from minimal sensor data.
The framework is tested on a problem relevant to vortex-induced vibration (VIV) energy harvesting systems: the turbulent flow around a one-degree-of-freedom moving cylinder. For this purpose we acquired velocity fields of an elastically mounted cylinder undergoing VIV in the cross-flow direction using time-resolved Particle Image Velocimetry (PIV). The acquired PIV measurements define a dataset of two-dimensional snapshots including the streamwise and crosswise velocity fields for a total of 17 operating conditions. To evaluate the model's generalization capability to unseen flow dynamics the test set comprises 5 operating conditions entirely separate from the training and validation sets.
When tested on two operating conditions of the test-set within the resonance region, the learned latent variables encode dynamical signatures characteristic of each flow regime. The latent space reveals stable annular orbits for the "lower branch" regime, characterized by highly periodic oscillations, and more irregular orbits for the "upper branch" regime, which exhibits a more irregular dynamics. This demonstrates that the latent space topology preserves significant information about the underlying flow physics while providing a geometrical interpretation of the flow dynamics.
The transformer predictions successfully capture these target attractor shapes, although volumetric contractions are observed, interpreted as implicit model regularization that prioritizes dominant dynamical structures over reproducing the full spectrum due to limited training data from the experimental dataset.
Upper Branch
Lower Branch
When VIVALDy is used in its inference phase, it reconstructs the turbulent velocity fields governing the vortex-induced vibration problem from just the cylinder displacement.
Comparing phase-averaged reconstructed flow fields to the acquired data from the test set shows that VIVALDy's predictions closely align with ground truth, accurately reproducing the coherent velocity structures that define the dominant wake topology. This demonstrates the framework's ability to capture essential flow physics from just the cylinder displacement signal.
Acquired Fields
Predicted Fields