A Physics-Informed Approach of Blood Flow and Wall Stress Estimation via Higher-Order ReLU Kolmogorov-Arnold Networks (HRKANs)

Quantifying near-wall blood flow and wall shear stress (WSS) in patient-specific geometries remains challenging due to uncertainties in boundary conditions, image segmentation, and sparse measurement data. Traditional CFD and experimental techniques (e.g., PIV) are highly sensitive to these uncertainties, limiting clinical adoption of WSS as a biomarker. We propose the first application of physics-informed Higher-order ReLU Kolmogorov-Arnold Networks (HRKANs) to estimate blood velocity and WSS from sparse interior velocity measurements with partially unknown inlet/outlet boundary conditions. HRKANs leverage smooth, higher-order differentiable activation functions optimized for GPU efficiency and accurate enforcement of the incompressible Navier-Stokes equations. Tested on 2D stenosis and aneurysm flows with only five interior sensors, HRKAN-based PINNs outperform standard MLP- and B-spline KAN-based PINNs in both velocity and WSS reconstruction under identical parameter budgets, achieving as much as 31 % and 23 % lower MSE respectively. Results demonstrate HRKANs' superior capability for ill-posed hemodynamic inverse problems.