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The authors construct a purely physics-driven Periodic Physics-Informed Neural Network (P-PINN) that models parametric periodic flows by enforcing exact temporal periodicity over a single cycle, completely bypassing computationally prohibitive transient time-marching simulations. By parameterizing continuous flow conditions and kinematics within the network, the aerodynamic model couples with structural dynamics via first-order harmonic balance to predict finite-amplitude aeroelastic responses without requiring pre-generated simulation training data. Validated on oscillating cylinders and airfoils at subcritical Reynolds numbers, the framework matches high-fidelity coupled CFD/CSD benchmarks while evaluating complete parametric aeroelastic response curves online in seconds.
Aeroelastic limit-cycle responses can now be resolved online in seconds without any pre-computed simulation data by enforcing single-cycle periodic boundary conditions directly inside physics-informed neural networks.
Periodic unsteady flows are common in forced-motion and fluid-structure interaction problems. Their parametric analysis typically requires repeated high-fidelity simulations, whereas existing reduced-order and surrogate models generally rely on pre-generated flow-field or aerodynamic data. This study proposes a purely physics-driven framework for solving parametric periodic flows and finite-amplitude aeroelastic responses. First, a Periodic Physics-Informed Neural Network (P-PINN) is developed to directly solve periodic flows by imposing temporal periodicity over a single motion cycle, thereby avoiding the need to resolve the long transient evolution preceding the establishment of the periodic state. The flow conditions and motion parameters are further incorporated as network inputs to construct continuous parametric representations of the periodic flow field and aerodynamic forces. On this basis, the parametric aerodynamic model is coupled with the structural dynamic equation through first-order harmonic balance to solve the response amplitude and frequency of a single-degree-of-freedom aeroelastic system. This framework is validated using forced-motion cases of a circular cylinder and an airfoil, demonstrating accurate reproduction of periodic aerodynamic forces, surface load distributions, and instantaneous flow fields under different flow and motion parameters compared with time-marching results. Furthermore, aeroelastic analysis is conducted for an elastically mounted circular cylinder at subcritical Reynolds numbers, and the resulting aeroelastic response agrees well with fully coupled CFD/CSD results. Once trained offline, the parametric model can be repeatedly evaluated for different structural parameter states, enabling the complete aeroelastic response curve to be obtained online within seconds, without repeated long-time fluid-structure interaction time marching.