Uncovering near-wall blood flow from sparse data with physics-informed neural networks

Abstract

Near-wall blood flow and wall shear stress (WSS) regulate major forms of cardiovascular disease, yet they are challenging to quantify with high fidelity. Patient-specific computational and experimental measurement of WSS suffers from uncertainty, low resolution, and noise issues. Physics-informed neural networks (PINNs) provide a flexible deep learning framework to integrate mathematical equations governing blood flow with measurement data. By leveraging knowledge about the governing equations (herein, Navier–Stokes), PINN overcomes the large data requirement in deep learning. In this study, it was shown how PINN could be used to improve WSS quantification in diseased arterial flows. Specifically, blood flow problems where the inlet and outlet boundary conditions were not known were solved by assimilating very few measurement points. Uncertainty in boundary conditions is a common feature in patient-specific computational fluid dynamics models. It was shown that PINN could use sparse velocity measurements away from the wall to quantify WSS with very high accuracy even without full knowledge of the boundary conditions. Examples in idealized stenosis and aneurysm models were considered demonstrating how partial knowledge about the flow physics could be combined with partial measurements to obtain accurate near-wall blood flow data. The proposed hybrid data-driven and physics-based deep learning framework has high potential in transforming high-fidelity near-wall hemodynamics modeling in cardiovascular disease.

Comment on os-2021-84

“…Crucially, this will ensure that forecasting remains significantly computationally cheaper than the usage of wave models. These methods have been successfully applied to the solving of differential equations in engineering (Niaki et al, 2021;Zobeiry, and Humfeld, 2021), analyzing blood flow (Arzani et al, 2021), and chaotic systems (Khodkar and Hassanzadeh, 2021). Relevant for the current discussion, these methods are also finding use in weather and climate modelling (Kashinath et al, 2021).…”

Physics-informed data based neural networks for two-dimensional turbulence

“…The effect of adding such additional information leads to the penalizing of nonphysical solutions. It has been successfully shown to perform well in recent studies 11,12 . Another concept of using separate PINN for each set of governing equations is also shown to perform better than a single PINN model for the entire system 13 .…”

“…The main difficulty arises from the necessity of large training points and neural network architectures which demand models that can run only on multi-GPU resources 12 . One possible way to overcome this difficulty is to use some training data points from existing solution from experiments or CFD simulations 11 . Recently, turbulent flows 12,15 in reduced domains have been studied using PINN based methods with a small percentage of training data.…”

Physics-informed Dyna-style model-based deep reinforcement learning for dynamic control

“…physics-informed neural networks (PINNs) [46], where the violation of the physical laws is penalized by incorporating the equation residuals into the network loss function. This simple idea has been applied in many scientific and engineering problems [47][48][49][50][51].…”