From RANS Prediction to Hydrofoil Optimization: A Benchmark of Neural Surrogates

Neural flow surrogates are usually compared by field error, although their practical value often lies in the designs they select. We compare a convolutional neural network U-Net (CNN-U-Net), a physics-informed neural network (PINN), a Fourier neural operator (FNO), and a deep operator network (DeepONet) on 381 OpenFOAM computational fluid dynamics (CFD) simulations of hydrofoils in water. Complete families form disjoint training, validation, and final-test sets, and every architecture is trained with three seeds. The models predict Reynolds-averaged Navier–Stokes (RANS) fields, lift, drag, and pressure-based cavitation-inception risk, and then drive the same four-parameter hydrofoil shape-optimization loop. DeepONet gives the lowest mean pressure, Cₚ, lift, and drag errors on the untouched test families; the PINN is close and has the fastest inference. Inference is 384–665 times faster than OpenFOAM. Across seeds, endpoint solves give mean L/D from 22.10 to 37.47, but a three-level grid study shows that drag remains mesh-sensitive. Field accuracy, force accuracy, search quality, and simulator verification are related but not interchangeable.