CARS: a centerline-anchored attention surrogate for coronary blood flow on skeleton-generated lumen geometries

When the parameter of a PDE surrogate is the flow domain itself, the key/value set of an attention model must encode that domain. We present CARS (Coronary Artery Rapid Surrogate), a learned surrogate for the finite-volume solution map of the steady incompressible Navier-Stokes equations on coronary lumens built from image-derived centerlines. CARS maps a centerline with per-point lumen radius and a scalar inlet flow rate to pressure and velocity at arbitrary query points. The attention focal set is the case’s own centerline, so geometry fusion costs $O(N{n}_f)$ rather than $O(N^2)$ in the number of evaluation points. Trained per territory on $\mathrm{2,700}$ OpenFOAM solutions with synthetic focal lesions, CARS reaches relative ${\mathrm{\ell }}_2$ errors of $0.120\mathrm{/}0.149$ (pressure/velocity) on left-coronary and $0.063\mathrm{/}0.119$ on right-coronary test sets, in $87$~ms per case against a solver wall-clock of $572$-$\mathrm{1,063}$~s. It outperforms four parameter-matched neural operators, and accuracy saturates eightfold below the operating focal count. Fractional flow reserve derived from the predicted pressure matches the CFD label at Pearson $r=0.941\mathrm{/}0.993$ and reproduces the $\mathrm{F}\mathrm{F}\mathrm{R}\le 0.8$ decision in $97.7\mathrm{\%}\mathrm{/}96.3\mathrm{\%}$ of held-out cases. The predicted velocity does not satisfy continuity closely enough for derived quantities, and the weights are territory-specific.