发表机构
German Aerospace Center (DLR); Airbus Operations（德国航空航天中心; 空客运营公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究非定常翼型空气动力学的时空预测问题，核心方法是将图神经网络与增强神经常微分方程结合形成GNODE，主要贡献是该方法能稳定准确地预测表面力，适合建模含外部输入的非线性时空系统。
AI 中文摘要
非定常气动现象，如阵风、湍流和流固相互作用，会在飞行中影响飞机。量化此类非定常气动效应对于设计、优化和认证至关重要。行业标准的计算流体动力学方法计算成本高或受线性等假设限制。机器学习方法经训练后能快速计算非线性关系，适合作为替代模型。通过在离散空间域上自回归应用图神经网络（GNN）可进行时空预测，但自回归GNN存在误差累积问题。本文表明将GNN与增强神经常微分方程相结合，能对俯仰翼型表面力进行时间上稳定的预测。名为GNODE的方法基于图神经常微分方程，比自回归GNN基线在时间上更稳定、空间上更平滑且整体更准确。在包含俯仰翼型模拟的数据集上进行测试，增加潜在维度可提高GNODE的表现力和准确性。该方法适用于对具有外部输入的非线性时空系统进行建模。
英文摘要
Unsteady aerodynamic phenomena, such as gusts, turbulence, and fluid-structure interactions affect an aircraft during flight. For design, optimisation and certification, it is indispensable to quantify such unsteady aerodynamic effects. Industry-standard computational fluid dynamics methods, such as solving the unsteady Reynolds-averaged Navier-Stokes equations or the linearized frequency domain method, are either computationally expensive or restricted by assumptions like linearity. Once trained, machine learning methods are capable of computing non-linear relationships very fast, making them suitable as surrogate models. By autoregressively applying graph neural networks (GNNs), operating on a discretised spatial domain, spatio-temporal predictions can be made. However, autoregressive GNNs suffer from error accumulation leading to unstable rollouts over time. Here we show that combining GNNs with augmented Neural Ordinary Differential Equations yields temporally stable predictions of the surface forces on a pitching airfoil. We found that our approach, called GNODE, based on Graph Neural Ordinary Differential Equations, provides temporally more stable, spatially smoother, and overall more accurate results than an autoregressive GNN baseline. Tests are conducted on a dataset consisting of a simulations of a pitching airfoil, including transonic shocks, transient behaviour and dynamic non-linearities. Augmenting GNODEs with additional latent dimensions improves the expressivity and accuracy by capturing underlying history effects. The developed method demonstrates an approach that is suitable to model non-linear spatio-temporal systems with exogenous inputs.
Comments27 pages, 18 figures, submitted to Computers & Fluids
