Integrating symbolic regression with physics-informed neural networks for simulating nonlinear wave dynamics in arterial blood flow

Abstract

This study explores a hybrid framework integrating machine learning techniques and symbolic regression via genetic programing for analyzing the nonlinear propagation of waves in arterial blood flow. We employ a mathematical framework to simulate viscoelastic arterial flow, incorporating assumptions of long wavelength and large Reynolds numbers. We used a fifth-order nonlinear evolutionary equation using reductive perturbation to represent the behavior of nonlinear waves in a viscoelastic tube, considering the tube wall's bending. We obtain solutions through physics-informed neural networks (PINNs) that optimizes via Bayesian hyperparameter optimization across three distinct initial conditions. We found that PINN-based models are proficient at predicting the solutions of higher-order nonlinear partial differential equations in the spatial-temporal domain [−1,1]×[0,2]. This is evidenced by graphical results and a residual validation showing a mean absolute residue error of O(10−3). We thoroughly examine the impacts of various initial conditions. Furthermore, the three solutions are combined into a single model using the random forest machine learning algorithm, achieving an impressive accuracy of 99% on the testing dataset and compared with another model using an artificial neural network. Finally, the analytical form of the solutions is estimated using symbolic regression that provides interpretable models with mean square error of O(10−3). These insights contribute to the interpretation of cardiovascular parameters, potentially advancing machine learning applications within the medical domain.