Data-driven Wall Shear Stress Prediction with 3D Near-Wall and Surface Transport Models

Accurate wall shear stress (WSS) measurement is essential in biomedical and cardiovascular flows. Estimating WSS in vascular flows necessitates detailed velocity field data near the vessel walls, which can be challenging due to experimental limitations such as resolution. This study explores using near-wall concentration measurements to derive WSS vectors through a data-driven approach. We compare two methods: a 3D near-wall region model with 3D conservation laws and a surface transport model where the 3D transport equations are projected to the wall, leveraging the close relationship between WSS and near-wall velocity. Physics-informed neural networks (PINNs) were used to solve the inverse problem and infer WSS from near-wall concentration data. Multiphysics CFD simulations provided synthetic concentration data in different benchmark problems, including a steady 2D backward-facing step, a pulsatile 3D constricted channel, and a pulsatile patient-specific coronary artery stenosis model. Our findings highlight the strengths and limitations of each approach in estimating WSS topology and magnitude.