Predicting Flow-Induced Vibration in Isolated and Tandem Cylinders Using Hypergraph Neural Networks

Abstract: We present a finite element-inspired hypergraph neural network framework for predicting flow-induced vibrations in freely oscillating cylinders. The surrogate architecture transforms unstructured computational meshes into node-element hypergraphs that encode higher-order spatial relationships through element-based connectivity, preserving the geometric and topological structure of the underlying finite-element discretization. The temporal evolution of the fluid-structure interaction is modeled via a modular partitioned architecture: a complex-valued, proper orthogonal decomposition-based sub-network predicts mesh deformation using a low-rank representation of Arbitrary Lagrangian-Eulerian (ALE) grid displacements, while a hypergraph-based message-passing network predicts the unsteady flow field using geometry-aware node, element, and hybrid edge features. High-fidelity ALE-based simulations provide training and evaluation data across a range of Reynolds numbers and reduced velocities for isolated and tandem cylinder configurations. The framework demonstrates stable roll-outs and accurately captures the nonlinear variation of oscillation amplitudes with respect to reduced velocity, a key challenge in surrogate modeling of flow-induced vibrations. In the tandem configuration, the model successfully resolves complex wake-body interactions and multi-scale coupling effects, enabling accurate prediction of pressure and velocity fields under strong wake interference conditions. Our results show high fidelity in reproducing force statistics, dominant frequencies, and flow-field dynamics, supporting the framework's potential as a robust surrogate model for digital twin applications.