The Degasperis-Procesi (DP) equation, is a prominent nonlinear partial differential equation (PDEs) with important applications in computational fluid dynamics (CFD) in particular wave propagation. It poses significant challenges when seeking accurate numerical solutions, especially in the context of boundary value problems. This article presents a novel approach for solving the boundary value problem associated with the DP equation utilizing Physics-informed Neural Networks (PINNs). Traditional numerical methods often struggle to capture the complex wave dynamics and steep gradients inherent in the DP equation. In contrast, PINNs leverage the power of artificial neural networks and physical principles to learn and approximate the underlying solution without relying on a predefined grid. This article contributes to the growing body of research in the application of machine learning techniques to solve challenging partial differential equations, particularly for problems where traditional numerical methods encounter limitations. Our PINN model has been able to reduce the computational cost. Though the undertaken problem is high dimension, but PINN does not suffer for curse of dimensionality.