Please use this identifier to cite or link to this item: http://hdl.handle.net/2080/4476
Title: Solving the Degasperis–Procesi Equation Boundary Value Problem Using Physics-Informed Neural Networks
Authors: Kumar, Sandeep
Sahoo, Arup Kumar
Chakraverty, S.
Keywords: Degasperis–Procesi equation
Physics-Informed Neural Networks
machine learning
numerical methods
fluid dynamics
Issue Date: Feb-2024
Citation: Latest Advances in Computational and Applied Mathematics-2024 (LACAM-24), IISER Thiruvananthapuram, Kerala, India, 21-24 February 2024
Abstract: The Degasperis– Procesi (DP) equation, a prominent nonlinear partial differential equation with important applications in fluid dynamics and wave propagation, 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 enables the accurate representation of the solution in regions where traditional methods falter. Our methodology involves training a neural network to minimize the residual of the DP equation along with enforcing boundary conditions, leading to a data-driven solution that seamlessly incorporates both the governing equation and boundary constraints. We demonstrate the effectiveness of this approach on a range of challenging DP equation boundary value problems. Through comprehensive numerical experiments, we showcase the ability of PINNs to accurately predict the solution of the DP equation while maintaining stability and computational efficiency. Furthermore, we highlight the flexibility of the approach in handling various boundary conditions and complex geometries. 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.
Description: Copyright belongs to proceeding publisher
URI: http://hdl.handle.net/2080/4476
Appears in Collections:Conference Papers

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