An Efficient and Accurate Surrogate Modeling of Flapping Dynamics in Inverted Elastic Foils using Hypergraph Neural Networks

TL;DR

This work tackles the challenge of predicting unsteady, strongly coupled fluid–structure dynamics of inverted elastic foils used for energy harvesting. It introduces a rotation-equivariant, quasi-monolithic hypergraph neural network surrogate that combines a solid sub-network based on complex-valued POD with a FE-inspired $\phi$-GNN fluid model, trained on high-fidelity ALE-based FSI data mapped to a node–element hypergraph. The approach yields accurate long-horizon predictions for foil displacement, hydrodynamic forces, and flow fields, while delivering more than two orders of magnitude speedup over full-order simulations. This enables real-time analysis, rapid design optimization, and control for energy-harvesting foil systems, with potential extension to foil arrays and wake-interaction studies. The framework preserves local conservation and geometric fidelity through FE-inspired hypergraph convolutions and achieves robust performance across a range of mass ratios $m^*$ and Reynolds numbers $Re$.

Abstract

Cantilevered elastic foils can undergo self-induced, large-amplitude flapping when subject to fluid flow, a widely observed phenomenon of fluid-structure interaction, from fluttering leaves or the movement of fish fins. When harnessed in steady currents, these oscillations enable the extraction of kinetic energy from the flow. However, accurately predicting these dynamics requires high-fidelity simulations that are prohibitively expensive to perform across the broad configuration space needed for design optimization. To address this, we develop a novel graph neural network (GNN) surrogate for the inverted foil problem, modeled as an elastically mounted rigid foil undergoing trailing-edge pitching in uniform flow. The coupled fluid-structure dynamics are solved using a Petrov-Galerkin finite element method with an arbitrary Lagrangian-Eulerian formulation, providing high-fidelity data for training and validation. The surrogate uses a rotation-equivariant, quasi-monolithic GNN architecture: structural mesh motion is compressed via proper orthogonal decomposition and advanced through a multilayer perceptron. At the same time, the GNN evolves the flow field consistent with system states. Specifically, this study extends the hypergraph framework to flexible, self-oscillating foils, capturing the nonlinear coupling between vortex dynamics and structural motion. The GNN surrogate achieves less than 1.5% error in predicting tip displacement and force coefficients over thousands of time steps, while accurately reproducing dominant vortex-shedding frequencies. The model captures energy transfer metrics within 3% of full-order simulations, demonstrating both accuracy and long-term stability. These results show a new, efficient surrogate for long-horizon prediction of unsteady flow-structure dynamics in energy-harvesting systems.

Figures (22)

• Figure 1: (a) Conversion from computational mesh to node-element hypergraph, (b) A diagram illustrating the graph neural network-based reduced order model using the quasi-monolithic framework trained on full order model time-series data
• Figure 2: Schematic of the computational domain used for generating the ground truth data
• Figure 3: Transverse tip displacement of the rigid foil at $m^* = 1$, $Re = 1000$ and $K^*_\theta = 2.4$
• Figure 4: (a) Computational mesh used for data generation with a close-up of the boundary layer mesh surrounding the rigid foil, and (b) coarse mesh used for the GNN model
• Figure 5: Transverse tip displacement, lift, and drag coefficients calculated from the fine finite element mesh and interpolated coarse GNN grid at $m^* = 0.5$, $Re = 1000$ and $K^*_{\theta} = 2.4$