Neural Differential Equations for Oscillatory Flows in Aeroelasticity Applied to Transonic Buffet

Abstract

Self-excited aerodynamic flows arise across a broad range of systems and can drive nonlinear fluid-structure interactions and aeroelastic instabilities that are challenging and computationally expensive to predict. This paper presents a physics-guided neural differential equation (DE) reduced order model (ROM) combining a nonlinear fluid oscillator, a finite-memory multi-input Volterra series, and a compact neural network correction. The multi-input aerodynamic formulation is generalized to m structural modes, capturing direct and nonlinear cross-modal coupling. The model is identified from a single prescribed-motion CFD simulation with simultaneous excitation of all retained structural modes, and is then coupled with the structural equations of motion for efficient aeroelastic prediction. Applied to transonic buffet over the ONERA OAT15A airfoil, the time-marching ROM predicts aeroelastic stability, frequency lock-in, and limit cycle amplitudes in good agreement with full-order reference solutions. The ROM is used to provide substantial new insight into buffet-induced aeroelastic instabilities involving more than one structural mode.