GNODE Predicts Unsteady Aerodynamics with Enhanced Stability

Understanding unsteady aerodynamic phenomena, such as those caused by gusts or turbulence, is critical for aircraft design and certification. Traditional computational fluid dynamics (CFD) methods are either too slow or rely on restrictive assumptions. Machine learning models offer a faster alternative, but autoregressive Graph Neural Networks (GNNs), while capable of spatio-temporal predictions, often suffer from error accumulation, leading to unstable long-term rollouts. This research introduces GNODE (Graph Neural Ordinary Differential Equations), a novel method designed to overcome these stability issues. GNODE integrates GNNs with augmented Neural Ordinary Differential Equations, which allows the model to learn continuous-time dynamics. This combination significantly improves the temporal stability of predictions for surface forces on a pitching airfoil. Tests conducted on a complex dataset involving transonic shocks and dynamic non-linearities demonstrated that GNODE provides more stable, spatially smoother, and overall more accurate results compared to standard autoregressive GNN baselines. The augmentation with additional latent dimensions further enhances GNODE's expressivity and accuracy by capturing underlying history effects. This method presents a promising approach for modeling complex non-linear spatio-temporal systems with external inputs, offering a faster and more reliable surrogate model for aerodynamic simulations.