Unsupervised Denoising and Super-Resolution of Vascular Flow Data by Physics-Informed Machine Learning

Area of Science:

• Fluid dynamics
• Machine learning
• Computational science

Background:

• Accurate flow field reconstruction is crucial in fluid dynamics.
• Existing methods often require high-resolution data or specific labels, limiting their applicability.
• Noise and low-resolution data are common challenges in experimental and simulated flows.

Purpose of the Study:

• To develop an unsupervised deep learning approach for simultaneous flow denoising and super-resolution.
• To demonstrate the model's capability in reconstructing complex 3D flows, including stenosis and aneurysm cases.
• To achieve high-fidelity flow reconstruction without relying on ground-truth high-resolution data.

Main Methods:

• Utilized auto-encoders for compressing flow domain geometry and flow field representations.
• Employed a physics-informed neural network conditioned on these compressed representations.
• Implemented a physics-based loss function incorporating Navier-Stokes equations for training.
• Generated ground truth data using computational fluid dynamics and introduced multiplicative Gaussian noise.

Main Results:

• Achieved mean squared errors of O(1.0 × 10-4) in true flow reconstruction.
• Obtained root mean squared residuals of O(1.0 × 10-2) for momentum and continuity equations.
• Demonstrated high correlation coefficients for hidden pressure (0.971) and wall shear stress (0.82).
• Successfully denoised and super-resolved flow fields up to 20x the input resolution.

Conclusions:

• The unsupervised deep learning method effectively denoises and super-resolves flow fields.
• The model generalizes to various complex 3D flow scenarios with different geometries and boundary conditions.
• This approach offers a powerful tool for enhancing flow data quality without the need for high-resolution labels.