Efficacy of the Weak Formulation of Sparse Nonlinear Identification in Predicting Vortex-Induced Vibrations

TL;DR

This paper demonstrates that the weak formulation of sparse nonlinear identification (WSINDy) effectively uncovers interpretable models of vortex-induced vibrations from data, especially for complex, aperiodic fluid-structure interactions.

Contribution

It introduces and validates the use of WSINDy as a robust, data-driven method for modeling VIV, outperforming standard approaches in handling aperiodic dynamics.

Findings

WSINDy provides more robust models for aperiodic VIV dynamics.

Data-driven models accurately capture the quantitative behavior of VIV.

POD analysis reveals dominant flow structures and reduced-dimensional dynamics.

Abstract

Vortex-induced vibrations (VIV) remain a canonical yet complex manifestation of fluid-structure interactions, where coupled nonlinear dynamics govern the motion of bluff bodies. For several years, we have relied on traditional reduced-order mathematical models derived from empirical and oscillator-based formulations; however, such models often fail to reproduce the quantitative dynamics observed in realistic flow environments. In this study, we explore a data-driven framework that leverages sparse identification of nonlinear dynamics (SINDy) and its weak formulation to uncover the governing equations of a single-degree-of-freedom cylinder undergoing VIV, using both data generated from previously developed reduced-order models and high-fidelity simulation results to assess the interpretation and efficacy of models discovered from a purely data-driven approach, particularly when the underlying dynamics are not fully known. The weak formulation (WSINDy), which replaces numerical differentiation with an integral-based representation, demonstrates marked robustness for aperiodic dynamics in particular. A complementary analysis using proper orthogonal decomposition (POD) is employed to extract the dominant spatio-temporal structures of the flow and to assess whether the temporal evolution of the wake can be represented on a reduced-dimensional manifold. The findings establish that data-driven identification can recover interpretable, quantitatively reliable models of VIV, providing a robust and computationally efficient pathway for modelling fluid-structure interactions directly from data. In particular, WSINDy is shown to be a more robust and interpretable alternative to standard SINDy for discovering VIV equations from aperiodic response dynamics, paving the way for predictive, data-informed design of fluid-structure interaction systems.