Physics-Informed Neural Networks for the High-Resolution Reconstruction of Flow Measurement Indicators in Fluid Dynamics

Jul 16, 2026

Accurate, spatially resolved flow field measurements underpin reliable hemodynamic assessment in cardiovascular research and clinical practice, yet common experimental methods such as 4D flow MRI, PIV, and Doppler ultrasound often provide sparse, noisy, and under-resolved data—especially near vessel walls and in complex flow regions. A physics-informed neural network (PINN) framework integrates the incompressible Navier–Stokes equations with measured velocity fields to reconstruct velocity, infer unmeasured quantities like pressure and wall shear stress, and improve spatial resolution. Results on nozzle and aneurysm models show closer agreement with ground truth than standard CFD or purely data-driven methods.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages30

Reading Time1 h 16 min

Introduction

4D flow MRI and hemodynamic biomarkers

Limits from resolution, noise, and boundary/time uncertainty

CFD as an alternative and its practical constraints

Paper objective: physics-informed machine learning for reconstruction

arXiv :2607 . 11576v1 [math .NA] 13 Jul 2026 Figure 1: Graphical abstract. We use physics-informed neural networks (PINNs) to integrate physical knowledge through the Navier–Stokes equations with spatially under-resolved blood flow velocity measurements. This enables us to derive additional hemodynamic insights and achieve a spatially resolved solution. Graphical Abstract Physics-Informed Neural Networks for the High-Resolution Reconstruction of Flow Measurement Indicators in Fluid Dynamics Irena Radišić, Raffaele Tirotta, Alberto Zingaro, Stefano Pagani, Luca Dede’ We use physics-informed neural networks (PINNs) to integrate physical knowledge through the Navier–Stokes equations with spatially under-resolved blood flow velocity measurements. This enables us to derive additional hemodynamic insights and achieve a spatially resolved solution. Physics-Informed Neural Networks for the High-Resolution Reconstruction of Flow Measurement Indicators in Fluid Dynamics Irena Radišićb,∗, Raffaele Tirottaa , Alberto Zingarob,c , Stefano Paganib , Luca Dede’b a Politecnico di Milano, Piazza Leonardo Da Vinci 32, Milan, 20133, Italy bMOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo Da Vinci 32, Milan, 20133, Italy cELEM Biotech S.L., Via Laietana 26, Barcelona, 08003, Spain Abstract Accurate, spatially resolved flow field measurements are essential for the reliable assessment of hemodynamic quantities in cardiovascular research and clinical practice. Experimental techniques, such as 4D flow MRI, PIV, or Doppler ultrasound, often yield data that are sparse, noisy, or under-resolved, particularly near vessel walls and in regions of complex flow. This limits the fidelity of distributed or derived hemodynamic indicators such as the wall shear stress and the clinical utility of such measurements. To address these challenges, we propose a physics-informed neural network (PINN) framework that integrates the incompressible Navier–Stokes equations with velocity measurements coming from experimental flow field data. By embedding physical laws into data, PINN enhances the reconstruction of velocity fields, enables the estimation of unmeasured quantities such as pressure and wall shear stress, and improves the spatial resolution of hemodynamic indicators. We show the effectiveness of our approach using both in silico and experimental data. First, we apply our method to the FDA nozzle benchmark, leveraging both control particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. Next, we apply our method to the more complex case of blood flow in an aneurysm model, exploiting in vitro 4D flow MRI data. In both cases, the synergy between data-driven learning and physics-based regularization yields results that align more closely with ground truth observations than standard CFD or pure data-driven approaches. Our findings highlight the potential of PINNs to improve the fidelity of under-resolved flow field measurements and yield spatially resolved hemodynamic indicators. Keywords: PINNs, 4D flow MRI, Computational hemodynamics, Scientific machine learning 1. Introduction 4D flow MRI is a clinically established and non-invasive imaging technique for the in vivo velocity measurement of cardiac and vascular flows [1–3] . It consists of a 3D time-varying description of the three components of the blood velocity vector field based on phase-contrast MRI [4] . The reconstructed spacetime description of the blood velocity provides hemodynamics biomarkers for diagnosis [5], including the wall shear stress, which is used to assess the risk of rupture in a blood vessel or to assist the diagnosis of important cardiac pathologies like stenosis or aneurysms [6, 7] . However, the accuracy in reconstructing biomarker indicators is constrained by the limited spatio-temporal resolution and signal-to-noise ratio [2] . Indeed, 4D flow MRI is not able to capture the small scales or flow-fi

FAQs

What is the main goal of the proposed PINN framework?

Reconstruct high-resolution velocity fields from under-resolved experimental flow measurements by embedding incompressible Navier–Stokes physical constraints into a physics-informed neural network.

Which hemodynamic quantities can the method estimate beyond the measured velocities?

It enables estimation of unmeasured quantities such as pressure and wall shear stress, improving the spatial resolution of derived hemodynamic indicators.

How is the approach validated in the document?

Effectiveness is demonstrated on both in silico and experimental cases, including the FDA nozzle benchmark (using PIV and CFD) and a blood-flow aneurysm model (using in vitro 4D flow MRI data).

Jul 16, 2026

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