Effects of viscosity and induced magnetic fields on weakly nonlinear wave transmission in a viscoelastic tube using physics-informed neural networks

Abstract

This study presents an advanced deep learning methodology that utilizes physics-informed neural networks (PINNs), to analyze the transmission of weakly nonlinear waves in a prestressed viscoelastic arterial tube. Using the long wave approximation, a mathematical model is constructed to replicate the propagation of weakly nonlinear waves in a viscoelastic arterial tube filled with viscous nanofluid, taking into account the influence of an induced magnetic field. The perturbed Burger, perturbed Korteweg–de Vries, and perturbed Korteweg–de Vries-Burgers equations are formulated based on the combined effects of nanofluid viscosity and the applied magnetic field using the reductive perturbation technique. Semi-supervised physics-informed neural network models are utilized to solve these perturbed evolutionary equations, trained on a limited dataset within their rectangular domain of definition. Gaussian process-based Bayesian optimization is used to determine the hyperparameters of the neural network, ensuring optimal model is performance. The effectiveness of the optimal models is evaluated by calculating the residual losses associated with the perturbed partial differential equations (PDEs). Visual representations of weakly non-linear wave propagation, considering nanofluid viscosity and induced magnetic fields, enhance the comprehension of dissipative effects in the cardiovascular system. These insights aid in obtaining precise measurements of pulse wave velocity for cardiovascular health monitoring. Consequently, the application of PINN proves to be a valuable tool for solving real-world PDEs and highlights its importance in advancing medical machine learning fields.