Please use this identifier to cite or link to this item: http://hdl.handle.net/2080/4476
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dc.contributor.authorKumar, Sandeep-
dc.contributor.authorSahoo, Arup Kumar-
dc.contributor.authorChakraverty, S.-
dc.date.accessioned2024-03-14T11:28:10Z-
dc.date.available2024-03-14T11:28:10Z-
dc.date.issued2024-02-
dc.identifier.citationLatest Advances in Computational and Applied Mathematics-2024 (LACAM-24), IISER Thiruvananthapuram, Kerala, India, 21-24 February 2024en_US
dc.identifier.urihttp://hdl.handle.net/2080/4476-
dc.descriptionCopyright belongs to proceeding publisheren_US
dc.description.abstractThe 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.en_US
dc.subjectDegasperis–Procesi equationen_US
dc.subjectPhysics-Informed Neural Networksen_US
dc.subjectmachine learningen_US
dc.subjectnumerical methodsen_US
dc.subjectfluid dynamicsen_US
dc.titleSolving the Degasperis–Procesi Equation Boundary Value Problem Using Physics-Informed Neural Networksen_US
dc.typePresentationen_US
Appears in Collections:Conference Papers

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