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The present work introduces a deep learning approach to describe the perturbations of the pressure and radius in arterial blood flow. A mathematical model for the simulation of viscoelastic arterial flow is developed based on the assumption of long wavelength and large Reynolds number. Then, the reductive perturbation method is used to derive nonlinear evolutionary equations describing the resistance of the medium, the elastic properties, and the viscous properties of the wall. Using automatic differentiation, the solutions of nonlinear evolutionary equations at different time scales are represented using state-of-the-art physics-informed deep neural networks that are trained on a limited number of data points. The optimal neural network architecture for solving the nonlinear partial differential equations is found by employing Bayesian Hyperparameter Optimization. The proposed technique provides an alternate approach to avoid time-consuming numerical discretization methods such as finite difference or finite element for solving higher order nonlinear partial differential equations. Additionally, the capability of the trained model is demonstrated through graphs, and the solutions are also validated numerically. The graphical illustrations of pulse wave propagation can provide the correct interpretation of cardiovascular parameters, leading to an accurate diagnosis and successful treatment. Thus, the findings of this study could pave the way for the rapid development of emerging medical machine learning applications. • The present work introduces a deep learning approach to describe the arterial blood flow. • An overview of deep learning-based solutions of nonlinear PDEs and error analysis of the proposed model has been described. • The prime factors such as medium resistance, elastic properties, and viscosity of the wall were taken into account. • The predicted solutions of the PDEs in the form of pressure pulses and solitary waves are discussed graphically. • The proposed technique provides an alternative approach to numerical methods for solving higher-order nonlinear PDEs. [ABSTRACT FROM AUTHOR]