Use of neural network and machine learning in optimizing heat transfer and entropy generated in a cavity filled with nanofluid under the influence of magnetic field: A numerical study

Shah, Murad Ali; Pan, Kejia; Ibrahim, Muhammad; Saeed, Tareq

doi:10.1016/j.enganabound.2022.03.012

Cited by 13 publications

(1 citation statement)

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“…When solving partial differential equations using traditional numerical methods, such as the Finite Difference Method (FDM) [ 6 ], Finite Element Method (FEM) [ 7 ], Finite Volume Method (FVM) [ 8 ], Radial Basis Function Method (RBF) [ 9 ], etc., problems such as high computational costs and the curse of dimensionality are often encountered. Over the last few years, the use of machine learning to solve partial differential equations has also rapidly expanded [ 10 , 11 , 12 , 13 ]. In 2018, Karniadakis and his research team were the first to put forward the concept of physics-informed neural networks (PINNs) [ 14 , 15 ], which solve PDEs by embedding them and their initial boundary value conditions in the loss function of the neural network thanks to automatic differentiation [ 16 ], following the physical laws described by nonlinear partial differential equations.…”

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confidence: 99%

A Second-Order Network Structure Based on Gradient-Enhanced Physics-Informed Neural Networks for Solving Parabolic Partial Differential Equations

Sun

Feng

2023

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Physics-informed neural networks (PINNs) are effective for solving partial differential equations (PDEs). This method of embedding partial differential equations and their initial boundary conditions into the loss functions of neural networks has successfully solved forward and inverse PDE problems. In this study, we considered a parametric light wave equation, discretized it using the central difference, and, through this difference scheme, constructed a new neural network structure named the second-order neural network structure. Additionally, we used the adaptive activation function strategy and gradient-enhanced strategy to improve the performance of the neural network and used the deep mixed residual method (MIM) to reduce the high computational cost caused by the enhanced gradient. At the end of this paper, we give some numerical examples of nonlinear parabolic partial differential equations to verify the effectiveness of the method.

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