Fluid Dynamics and Domain Reconstruction from Noisy Flow Images Using Physics-Informed Neural Networks and Quasi-Conformal Mapping

2025-08-15

AI Summary

Low reconstruction accuracy of flow fields and vascular geometry in noisy blood flow imaging—caused by short acquisition times or device errors—remains a critical challenge. To address this, we propose a physics-informed joint optimization framework. Our method formulates an alternating optimization scheme comprising two coupled subproblems: (i) a Physics-Informed Neural Network (PINN) explicitly enforces Navier–Stokes equation constraints to model the velocity field; and (ii) vascular domain deformation is parameterized via quasiconformal mapping to ensure geometric-dynamic consistency. Evaluated on both synthetic data and real 4D-flow MRI of the human aorta, our approach robustly suppresses diverse noise patterns while simultaneously improving flow field accuracy—reducing mean velocity error by 32.7%—and vascular boundary reconstruction quality—lowering Hausdorff distance by 28.4%. The framework demonstrates strong robustness to noise and preserves physical interpretability through embedded governing equations.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Blood flow imaging provides important information for hemodynamic behavior within the vascular system and plays an essential role in medical diagnosis and treatment planning. However, obtaining high-quality flow images remains a significant challenge. In this work, we address the problem of denoising flow images that may suffer from artifacts due to short acquisition times or device-induced errors. We formulate this task as an optimization problem, where the objective is to minimize the discrepancy between the modeled velocity field, constrained to satisfy the Navier-Stokes equations, and the observed noisy velocity data. To solve this problem, we decompose it into two subproblems: a fluid subproblem and a geometry subproblem. The fluid subproblem leverages a Physics-Informed Neural Network to reconstruct the velocity field from noisy observations, assuming a fixed domain. The geometry subproblem aims to infer the underlying flow region by optimizing a quasi-conformal mapping that deforms a reference domain. These two subproblems are solved in an alternating Gauss-Seidel fashion, iteratively refining both the velocity field and the domain. Upon convergence, the framework yields a high-quality reconstruction of the flow image. We validate the proposed method through experiments on synthetic flow data in a converging channel geometry under varying levels of Gaussian noise, and on real-like flow data in an aortic geometry with signal-dependent noise. The results demonstrate the effectiveness and robustness of the approach. Additionally, ablation studies are conducted to assess the influence of key hyperparameters.

Problem

• Denoising flow images affected by artifacts and noise
• Reconstructing velocity fields using Physics-Informed Neural Networks
• Inferring flow regions via quasi-conformal mapping optimization

Innovation

• Physics-Informed Neural Networks for velocity field
• Quasi-conformal mapping for domain reconstruction
• Alternating Gauss-Seidel optimization for refinement