Pinning down the accuracy of physics-informed neural networks under laminar and turbulent-like aortic blood flow conditions.

BACKGROUND

Physics-informed neural networks (PINNs) are increasingly being used to model cardiovascular blood flow. The accuracy of PINNs is dependent on flow complexity and could deteriorate in the presence of highly-dynamical blood flow conditions, but the extent of this relationship is currently unknown. Therefore, we investigated the accuracy and performance of PINNs under a range of blood flow conditions, from laminar to turbulent-like flows.

METHODS

A stenosis was virtually induced in the thoracic segment of a patient's aorta to represent aortic coarctation. Stenosis severity was varied from 0% to 70% in increments of 5% (N=15 cases), corresponding to stenotic Reynolds number that ranged from 1000 to 3333. CFD simulations at high spatial and temporal resolutions (6.9 million mesh, 10,000 time-steps) were performed for all N=15 cases to obtain ground-truth velocity data. Fourier-based activation function in feed-forward PINNs with dynamic loss coefficients were trained to reconstruct CFD velocity field. Losses included those from physical equations, boundary conditions and sensor data sampled evenly from CFD simulations. Number of sensor points were increased from 200-1600 in increments of 200. This resulted in a total of 8 sensor point variations for each stenotic model (N=8). Hence, a total of 120 (NxN) cases were trained in this study. The PINNs architecture and data have been made open-sourced.

RESULTS

PINNs errors increased substantially for stenosis severity >50% (stenotic Reynolds numer > 2000) due to the presence of complex turbulent-like flow features. When using 400 sensor points, PINNs velocity magnitude errors ranged from 30% for no-stenosis model to 57% for the model with 70% stenosis, and dropped to 10% and 20%, respectively when the number of sensor points were increased to 1600. PINNs velocity magnitude errors increased monotonically with turbulent intensity, particularly beyond stenosis severity of 50%.

CONCLUSIONS

Our findings indicate that the accuracy of PINNs is dependent on the complexity of blood flow conditions. Using conventional PINNs architecture, the errors in trained velocity can increase substantially in the presence of turbulent-like blood flows that are typically found in various vascular pathologies.