2026 Mehta Airfoil Flow Routed Neural Operator

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 AirRANS benchmark, DD-RNO cuts velocity field mean-square error (MSE) by 17× (u) and 12× (u) over the strongest baseline, widening to 23× 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× relative to conventional pressure integration and raises drag 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×, and removing LCQ increases relative drag error more than 40×. At ~144 ms per sample—a 10,000× speedup over conventional RANS solvers—DD-RNO offers a su.