ANN-based methods for solving partial differential equations: a survey

Pratama, Danang A.; Bakar, Maharani A.; Ismail, Nur Baini; Mashuri, M

doi:10.1080/25765299.2022.2104224

Cited by 2 publications

(2 citation statements)

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“…Activation functions are widely employed to facilitate diverse computations between layers. Common activation functions include sigmoid or logistic, hyperbolic tangent (tanh), rectified linear unit (ReLU), and Leaky ReLU [21]. In this study, the hyperbolic tangent function (tanh) is chosen due to its demonstrated ability to yield superior results compared to alternative activation functions.…”

Section: Construction Of the Neural Network Architecturementioning

confidence: 99%

“…The backpropagation neural network is a type of ANN that is widely used for supervised learning tasks [16][17][18][19]. The basic idea behind the backpropagation neural network is to train the network to learn mapping between input data and their corresponding target outputs [20][21][22]. The training process involves adjusting the weights and biases of the network in order to minimize the difference between the predicted outputs and the actual target outputs.…”

Section: Introductionmentioning

confidence: 99%

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A Novel ANN-Based Radial Basis Function Collocation Method for Solving Elliptic Boundary Value Problems

Liu,

2023

Mathematics

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Elliptic boundary value problems (BVPs) are widely used in various scientific and engineering disciplines that involve finding solutions to elliptic partial differential equations subject to certain boundary conditions. This article introduces a novel approach for solving elliptic BVPs using an artificial neural network (ANN)-based radial basis function (RBF) collocation method. In this study, the backpropagation neural network is employed, enabling learning from training data and enhancing accuracy. The training data consist of given boundary data from exact solutions and the radial distances between exterior fictitious sources and boundary points, which are used to construct RBFs, such as multiquadric and inverse multiquadric RBFs. The distinctive feature of this approach is that it avoids the discretization of the governing equation of elliptic BVPs. Consequently, the proposed ANN-based RBF collocation method offers simplicity in solving elliptic BVPs with only given boundary data and RBFs. To validate the model, it is applied to solve two- and three-dimensional elliptic BVPs. The results of the study highlight the effectiveness and efficiency of the proposed method, demonstrating its capability to deliver accurate solutions with minimal data input for solving elliptic BVPs while relying solely on given boundary data and RBFs.

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Section: Construction Of the Neural Network Architecturementioning

confidence: 99%