AI 中文总结
该研究提出DD-RNO模型，通过域路由机制与学习型标准求积解决翼型流动预测瓶颈，在AirfRANS基准测试中精度显著优于基线且速度大幅提升，可用于实时气动设计优化。
AI 中文摘要
深度学习代理模型在翼型周围的RANS流动预测中面临两个长期瓶颈：单一神经架构无法同时解析陡峭的近壁边界层与平缓的远场势流；此外，基于连续场近似计算壁法向速度梯度时的数值不稳定性会削弱力的预测效果。DD-RNO（域分解路由神经算子）解决了这两个问题，它结合了谱几何编码器与两项物理引导的创新：（a）可微域路由机制，将流场划分为无粘区、边界层区和尾流区，并将查询点分配给专门的区域解码器；（b）学习型标准求积（LCQ），该机制用流场条件驱动的学习型积分权重替代不稳定的压力积分，直接从表面压力预测升力与阻力。在AirfRANS基准测试中，DD-RNO的速度场均方误差（MSE）较最强基线降低了17倍（u_x）和12倍（u_y），在分布外雷诺数外推场景下该倍数扩大至23倍，证明路由机制凭借其编码的物理规律实现了泛化，而非仅拟合训练分布；LCQ较传统压力积分将阻力MSE降低7.5倍，并将阻力秩相关系数从ρ=0.250提升至ρ=0.997。 ablation实验证实两个组件对性能均不可或缺：移除域路由会使速度误差增加8.2倍，移除LCQ会使相对阻力误差增加40倍以上。DD-RNO的单样本推理时间约为144毫秒，较传统RANS求解器提速10000倍，可为气动设计与优化循环提供足够准确且快速的代理模型。
英文摘要
Deep learning surrogates for RANS flow prediction around airfoils face two persistent bottlenecks. A single neural architecture cannot simultaneously resolve sharp near-wall boundary layers and smooth far-field potential flow. Additionally, force prediction is undermined by the numerical instability of computing wall-normal velocity gradients from continuous-field approximations. Both of these points are addressed with a DD-RNO (domain-decomposed routed neural operator), combining a spectral geometry encoder with two physics-guided innovations: (a) a differentiable domain routing mechanism that partitions the flow field into inviscid, boundary-layer, and wake regimes---dispatching query points to specialized regional decoders, and (b) learned canonical quadrature (LCQ), which replaces unstable pressure integration with flow-conditioned, learned integration weights that predict lift and drag directly from surface pressure. On the AirfRANS benchmark, DD-RNO cuts velocity field mean-square error (MSE) by 17$x$ ($u_x$) and 12$x$ ($u_y$) over the strongest baseline, widening to 23$x$ under out-of-distribution Reynolds extrapolation---evidence that the routing mechanism generalizes with the physics it encodes rather than merely fitting the training distribution. LCQ reduces drag MSE by 7.5$x$ relative to conventional pressure integration and raises drag rank correlation from $ρ= 0.250$ to $ρ= 0.997$. Ablations confirm that both components are indispensable to performance: removing domain routing increases velocity error by 8.2$x$, and removing LCQ increases relative drag error more than 40-fold. At ~144 ms per sample---a 10,000$x$ speedup over conventional RANS solvers---DD-RNO offers a surrogate accurate and fast enough for real-time aerodynamic design and optimization loops.
