A graph neural network based reduced-order model for flapping dynamics

An elastic foil, cantilevered at the trailing edge, experiences self-induced flapping when exposed to fluid flow. This fluid-structure interaction phenomenon has potential applications in renewable energy harvesting. We numerically examine the foil's response under wake interference when placed behind a stationary circular cylinder. The system is modeled using a higher-order variational finite element method based on coupled three-dimensional Navier-Stokes and nonlinear structural equations. In this setup, the foil shows early onset of flapping instability and undergoes sustained oscillations, synchronized with the cylinder wake [1].

We aim to conduct parameter optimization on the inverted foil system to maximize energy output, for which traditional computational simulations are time-consuming and computationally expensive. To this end, we propose a finite element-inspired graph neural network-based reduced order model (GNN-ROM) that can serve as a surrogate model for the inverted foil problem. Our model uses the rotation equivariant, quasi-monolithic GNN [2]. In this framework, proper orthogonal decomposition is used to extract select coefficients describing the mesh motion which are predicted over time using multilayer perceptrons, while the flow field is evolved based on the system state using the GNN. The structural state is modeled implicitly by the movement of the mesh on the solid-fluid interface. The proposed model will be evaluated using our full-order simulation data.