A Hybridized Approach on Physics Informed Neural Networks and Symbolic Regression for Simulating Nonlinear Wave Dynamics in Arterial Blood Flow

作     者：Changdar, Satyasaran Bhaumik, Bivas Sadhukhan, Nabanita Pandey, Sumit Mukhopadhyay, Sabyasachi De, Soumen Bakalis, Serafim 

作者机构：Department of Food Science University of Copenhagen Copenhagen Denmark Department of Mathematics National Institute of Technology Odisha Rourkela India Department of Applied Mathematics University of Calcutta 92 A.P.C. Road Kolkata India Department of Computer Science University of Copenhagen Copenhagen Denmark Centre For Computational And Data Sciences Indian Institute of Technology Kharag India 

出 版 物：《SSRN》 

年 卷 期：2024年

核心收录：

主　　题：Genetic programming 

摘      要：This study explores a comprehensive hybrid framework integrating machine learning techniques and symbolic regression via genetic programming 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 derive 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), an artificial intelligence (AI)-driven approach that optimizes via Bayesian hyperparameter optimization across three distinct initial conditions. We found that physics-informed neural network-based models are proficient at predicting the solutions of higher-order nonlinear partial differential equations in the spatial-temporal domain [-1,1] x [0,2]. This is evidenced by graphical results and a residual validation showing a mean absolute residue error of O(0.001). 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, a type of AI that provides interpretable models. These insights contribute to the interpretation of cardiovascular parameters, potentially advancing AI-driven machine learning applications within the medical domain. © 2024, The Authors. All rights reserved.