Operator learning for hemodynamics on variable domains: 2D stenosis and bifurcation.

We study neural-operator surrogates for steady incompressible Navier-Stokes flow on variable two-dimensional coronary-like domains. Two finite-element datasets are constructed: stenosed channels and bifurcating vessels, each with 1000 geometries. We compare a reference-domain MIONet based on diffeomorphic registration with geometry-aware point-cloud operators, GNOT and PCNO. PCNO gives the strongest in-distribution accuracy and best extrapolation to unseen inflow velocities, whereas MIONet is most stable under the tested OOD shape shift and fastest per forward pass. Currents-based geometric dissimilarity helps characterize error trends and supports reliability-aware surrogate assessment.