This paper introduces a data‑driven framework for long‑term prediction of fluid‑structure interaction (FSI) dynamics, focusing on flow‑induced vibration (FIV) of a flexible plate. The centerpiece is a stiffness‑conditioned neural evolution operator that jointly models the Eulerian flow field and the Lagrangian structural state. The plate is encoded by 101 ordered structural tokens, each carrying nodal coordinates and velocities, while the nondimensional bending stiffness serves as a global conditioning variable.
A hybrid CNN‑Transformer architecture employs bidirectional cross‑attention to couple fluid and structural representations. The operator is trained with staged multi‑step autoregressive rollouts and symmetry‑reflected trajectories, enabling a single model to capture three stiffness‑dependent response regimes: deflected‑flapping, deflected only, and flapping only. Predicted trajectories preserve the principal flow structures, structural oscillations, and dominant frequencies, and remain bounded even in blind 1000‑step rollouts. The operator also interpolates to stiffness values not seen during training.
To reduce sensitivity to under‑resolved near‑wall gradients in force reconstruction, we develop a differentiable aerodynamic‑force module based on the derivative‑moment transformation (DMT). Conventional wall‑stress surface integrals are replaced by an enclosed 2D curve integral around the core vortex region, allowing accurate lift and drag reconstruction. A signed distance function (SDF) and a smoothed Dirac‑delta formulation make the integration fully differentiable while preserving gradient flow.
The proposed framework provides an accurate and differentiable surrogate for stiffness‑dependent FSI dynamics, enabling efficient parameter studies and paving the way for stiffness optimization in flow‑energy‑harvesting applications.
Review