Super-resolution and denoising of vascular flow data by physics-informed machine learning*

We present the super-resolution and denoising of vascular flows using a deep learning model that does not require high resolution labels. The purpose of this model is to improve the resolution and fidelity of sparse and noisy flow measurements, as well as aid in the recovery of hidden quantities such as pressure or wall shear stress. The model is composed of 3 main components: a geometry autoencoder, a flow autoencoder and a phyics-informed neural network (PINN). A segmentation is performed on the noisy flow volume to identify the flow domain and a signed distance field to the flow boundary. Subsequently, a convolutional neural network (CNN) autoencoder is trained from signed-distance fields with a mean average error (MAE) loss on a noisy training dataset. Similarly a separate CNN is used for a flow autoencoder whose input is the 3-component, 3-dimensional fluid velocity field from the training dataset, again using a MAE loss. A PINN is developed to combine latent representations from the geometry and flow autoencoders to provide a pointwise estimate of the velocity and pressure at a given set of sample points. The PINN uses a multilayer perceptron and is trained using a reconstruction loss from the data and a PDE loss from evaluation of the Navier Stokes equations. The model was tested on stenotic and anuerysmal vascular flows computed from CFD and then downsampled and corrupted by noise to simulate measurements. We demonstrate model performance in comparison with a baseline CNN. In particular we demonstrate the ability of the proposed PINN to effectively denoise and super-resolve flow fields of different Reynolds numbers and for different geometries. In addition, demonstrate the ability of this model to recover well correlated pressure and wall shear stress fields.