Direct solution method for finite element analysis using Hopfield neural network

Yamashita, Hideo; Kowata, N.; Čingoski, Vlatko; Kaneda, Kazufumi

doi:10.1109/20.376426

Cited by 19 publications

(11 citation statements)

References 6 publications

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“…Another important reason for choosing (20) as the input-output function is that, the first derivations of both the original sigmoid function and our function are always positive [32].…”

Section: B Architecture For Mhfd Networkmentioning

confidence: 99%

Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques

Dehghan

Nourian

Menhaj

2008

Numerical Methods Partial

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One property of the Hopfield neural networks is the monotone minimization of energy as time proceeds. In this article, this property is applied to minimize the energy functions obtained by finite difference techniques of the Helmholtz-equation. The mathematical representation and correlation between finite difference techniques and modified Hopfield neural networks of the Helmholtz equation are presented. Significant advantages of the above method are its parallel, robust, easy programming nature, and ability of direct hardware implementation. Results of numerical simulations are described and analyzed to demonstrate the method. The results obtained using the proposed method show a very good agreement with theoretical and numerical solutions.

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“…Another important reason for choosing (20) as the input-output function is that, the first derivations of both the original sigmoid function and our function are always positive [32].…”

Section: B Architecture For Mhfd Networkmentioning

confidence: 99%

Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques

Dehghan

Nourian

Menhaj

2008

Numerical Methods Partial

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“…Knowing that this HNN should mimic a vectorial -relation, the G-nodes are assumed to represent a collection of scalar relations oriented along all possible 2-D directions. In other words (4) From (3) and (4) and by assuming an applied field along the axis, the activation function for the case of isotropic media may be determined from (5) For an activation function in the form , we get…”

Section: Proposed Hopfield Neural-network Approachmentioning

confidence: 99%

“…It should be pointed out that this particular feature makes it possible to obtain a solution for the 2-D magnetization distribution directly from neuron outputs in nonlinear media. This may be regarded as a unique Manuscript feature of this work in comparison with previous HNN representations in terms of one-dimensional (1-D) potentials that dealt with linear media (refer, i.e., to [5], [6]). In all cases, well-established HNN algorithms lead to automated solutions based on a minimum energy criterion.…”

Section: Introductionmentioning

confidence: 97%

Automated two-dimensional field computation in nonlinear magnetic media using Hopfield neural networks

Adly¹,

Abd-El-Hafiz²

2002

IEEE Trans. Magn.

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It is well known that the computation of magnetic fields in nonlinear magnetic media may be carried out using different approaches. In the case of problems involving complex geometries and/or magnetic media, numerical techniques become especially more appealing. In this paper, we present an automated integral equation approach using which two-dimensional field computations may be carried out in nonlinear magnetic media. This approach is constructed in terms of a continuous Hopfield neural network (HNN) whose neuron activation functions are set to mimic the vectorial magnetic properties of the media. Using well-established HNN energy minimization algorithms, an automated solution of the problem is then obtained. The approach has been implemented and resulted in good agreement with finite-element (FE) computations. Details of the approach, computations, and FE results are given in this paper.Index Terms-Continuous Hopfield neural networks, nonlinear magnetic media, 2-D field computations.

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“…An ideal solution is the combination of the accuracy of FEM and the rapidness of neural networks. Some literature introduces finite-element neural network (FENN) models combining FEM with neural networks [12]- [15]. But a neural network has not been used to simulate the whole process of FEM analysis in this research.…”

Section: Introductionmentioning

confidence: 97%

Finite-Element Neural Network-Based Solving 3-D Differential Equations in MFL

Wang

et al. 2012

IEEE Trans. Magn.

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The solution of a differential equation contains the forward model and the inverse problem. The finite element method (FEM) and the iterative approach based on FEM are extensively used to solve varied differential equations. Although FEM could obtain an accurate solution, the shortcoming of the approach is the high computational costs. This paper proposes an improved finite-element neural network (FENN) embedding a FEM in a neural network structure for solving the forward model while a conjugate gradient (CG) method is employed as the learning algorithm. Taking the 3-D magnetic field analysis in magnetic flux leakage (MFL) testing as an example, the comparison between CG algorithm and the gradient descent (GD) algorithm is presented. The vector plot of magnetic field intensity is obtained, and the vertical components of magnetic flux density are respectively analyzed. The iterative approach based on FENN and parallel radial wavelet basis function neural network is also adopted to solve the inverse problem. This approach iteratively adjusts weights of the inverse network to minimize the error between the measured and predicted values of MFL signals. The forward and inverse results indicate that FENN and the iterative approach are feasible methods with rapidness, accuracy and stability associated with 3-D different equations in MFL testing.Index Terms-Conjugate gradient (CG) algorithm, finite-element method (FEM), finite-element neural network (FENN), forward model, inverse problem, magnetic flux leakage (MFL) testing.

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Direct solution method for finite element analysis using Hopfield neural network

Cited by 19 publications

References 6 publications

Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques

Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques

Automated two-dimensional field computation in nonlinear magnetic media using Hopfield neural networks

Finite-Element Neural Network-Based Solving 3-D Differential Equations in MFL

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