arXiv:2606.06313physics.flu-dyncs.LG2026-06

用浓度数据反推血管壁剪切应力,两种新方法各有优劣。

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

论文配图:Wall Shear Stress Reconstruction from Concentration: Differentiable Physics and Physics-Informed Neural Networks
图 1 · 摘自论文原文
  • 基于物理约束的优化与神经网络结合,从有限浓度观测重建流场。
  • 近壁测量时两者都准,远场测量时传统神经网络失效,新方法仍有效。
  • 适合心血管流体分析,尤其适用于难测速度的临床场景。

壁面剪切应力(WSS)主导近壁物质输运,是心血管流体中的关键生物力学指标,但因其需精确计算近壁速度梯度而难以准确推断。被动标量场(如浓度或温度)随同一速度场输运,具备揭示隐藏流场物理量(如WSS)的潜力。本文采用两种根本不同的逆问题框架:基于离散伴随的可微分物理框架(强约束控制方程),以及物理信息神经网络(PINNs,软约束)。在二维后向台阶(2D-BFS)和三维患者特异性狭窄冠状动脉两个基准问题上测试。2D-BFS中,三种测量场景(近壁、远场、联合)下,当存在近壁数据时PINN精度高,但仅远场数据时失败;而可微分物理方法在所有场景均准确恢复WSS。在3D患者病例中,该方法优于PINNs,实现高精度重构。结果表明,测量位置与逆问题形式共同决定标量基近壁流推断的保真度。所提框架为从标量输运数据估计近壁血流动力学提供了路径,适用于可观察被动标量的各类流体问题。

原文摘要 · Abstract (English)

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.

流体仿真物理信息网络医学成像

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