Physics-Informed Neural Networks for Second-Order Porous Medium and Third-Order Korteweg-de Vries Equations
Patel, Pavan Yadav, Saroj
Patel, Pavan
Yadav, Saroj
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2026-03-01
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Abstract
Deep learning techniques have found diverse applications, including solving partial differential equations (PDEs). This chapter observes the utilization of physics-informed neural networks (PINNs) for solving a range of PDEs related to fluid dynamics applications. PINNs harness the inherent physical insights embedded within PDEs by integrating them as regularization terms, thereby optimizing the performance of neural networks. Notably, PINNs prove effective in handling higher-dimensional differential equations, offering substantial reductions in computational costs. The current chapter focuses on the application of PINNs to solve specific instances of fluid dynamics problems, including second-order porous medium and third-order Korteweg-de Vriesequations. The proposed methodology incorporates the Adam optimizer and employs the “tanh” activation function.
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Advances and Applications of Machine Learning in Fluid Flow Problems