A Graph Neural Network Based Surrogate Model for Flapping-Driven Ocean Energy Harvesting

Abstract Cantilevered elastic foils or panels can undergo self-induced large-amplitude flapping oscillations when submerged in a flowing fluid. This canonical phenomenon of fluid-structure interaction, commonly observed in nature, such as in fluttering leaves or fish fins, offers a promising mechanism for ocean energy harvesting. By leveraging the repetitive flapping motion, elastic foils can harness the abundant kinetic energy present in marine environments, including steady ocean currents and unsteady wave-driven flows. The efficiency of energy harvested by these foils is dictated by the amplitude and frequency of the oscillation, which are influenced by interactions with the surrounding flow. Optimizing these parameters is crucial for maximizing energy conversion efficiency and designing robust systems. However, high-fidelity simulations required for optimization over a wide parameter space are computationally expensive. To address this challenge, we propose a graph neural network-based surrogate model (GNN-ROM) tailored for the inverted foil problem. This model effectively handles mesh-structured data from full-order simulations without modifications, enabling efficient and accurate fluid-structure interaction simulations. The inverted foil is modeled as an elastically mounted rigid foil that undergoes a pitching motion around its trailing edge in uniform flow. The coupled fluid-structure system is simulated using a high-fidelity Petrov-Galerkin finite element approach, leveraging the arbitrary Lagrangian-Eulerian (ALE) formulation for precise interface tracking. The high-fidelity simulations serve as ground truth data for the training and evaluation of neural networks. Our deep learning model utilizes a rotation equivariant, quasi-monolithic GNN architecture based on the ALE formulation, wherein the coupled system dynamics are predicted with two sub-networks. First, essential coefficients describing mesh motion are extracted by proper orthogonal decomposition, which are predicted over time using a single multilayer perceptron. Moreover, the GNN-ROM evolves the flow field according to the state of the system. This approach effectively simulates coupled FSI dynamics, offering a robust surrogate model for rapid parametric optimization and control of energy harvesting devices based on inverted foil configurations.