Wall Shear Stress Reconstruction from Concentration: Differentiable Physics and Physics-Informed Neural Networks

2026-06-04

AI Summary

Accurate inference of wall shear stress (WSS) is hindered by the difficulty in obtaining near-wall velocity gradients. This work presents the first systematic comparison between differentiable physics—formulated as PDE-constrained optimization via discrete adjoints—and physics-informed neural networks (PINNs) for inverse modeling of WSS using only observations of passive scalar fields (e.g., concentration). The former enforces governing equations as hard constraints, while the latter treats them as soft penalties. Evaluated on two-dimensional backward-facing step flows and three-dimensional patient-specific coronary artery models, differentiable physics consistently achieves high-fidelity WSS reconstruction across diverse measurement configurations, whereas PINNs succeed only when near-wall data are included and fail with far-field measurements alone. These findings demonstrate that both sensor placement and modeling paradigm critically influence reconstruction accuracy, highlighting the superiority of differentiable physics for near-wall flow inference driven solely by scalar field data.

Abstract

Wall shear stress (WSS) governs near-wall transport dynamics and is a key hemodynamic indicator in cardiovascular flows, yet remains difficult to infer accurately due to the need for precise computation of near-wall velocity gradients. Passive scalar fields, such as concentration or temperature, are advected by the same underlying velocity field and have the potential to uncover hidden flow physics metrics such as WSS. In this work, we demonstrate such reconstruction from spatially limited passive scalar observations using two fundamentally different inverse frameworks: a differentiable physics framework based on discrete adjoint, PDE-constrained optimization, which enforces the governing equations as hard constraints, and physics-informed neural networks (PINNs), which treat them as soft constraints. Benchmark problems include a 2D canonical backward-facing step (2D-BFS) and a 3D patient-specific stenotic coronary artery. For the 2D-BFS case, evaluated under three measurement scenarios (near-wall, far-field, and combined), PINN achieves high accuracy when near-wall data are available but fails when restricted to far-field measurements, whereas the differentiable physics approach recovers accurate WSS across all scenarios. In the 3D patient-specific case, the differentiable physics framework outperforms PINNs, yielding accurate WSS reconstruction. These results establish that measurement location and inverse formulation jointly determine reconstruction fidelity in scalar-based near-wall flow inference. The proposed framework opens a path toward estimation of near-wall hemodynamics from scalar transport data, with broader applicability to fluid flow problems where passive scalars can be observed.

Problem

• Wall Shear Stress
• Passive Scalar
• Inverse Problem
• Near-wall Flow
• Hemodynamics

Innovation

• wall shear stress reconstruction
• differentiable physics
• physics-informed neural networks
• passive scalar
• inverse problem