Connectionist Learning Models for Application Problems Involving Differential and Integral Equations

Mall, Susmita; Jeswal, Sumit Kumar; Chakraverty, Snehashish

doi:10.1002/9781119585640.ch1

Cited by 2 publications

(3 citation statements)

References 35 publications

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“…The true solution is (29), the delay term τ = 1. Similarly, we divide the interval [0, 3] into three segments [0, 1], [1,2] and [2,3] to solve.…”

Section: Example 2 Consider the Variable Coefficients Linear Didaesmentioning

confidence: 99%

“…The simulation effect of approximate solution is shown in Figure 4. Next, Table 2 shows the relative errors of x(t) and y(t) when using CNN method and Tanh multi-layer neural network method to approximate model (29). The results show that the relative errors using CNN method can be as high as 1e − 12 and as low as 1e − 08, while the highest of Tanh multi-layer neural network is only 1e − 05, so this results prove that the CNN method still has good results for linear DIDAEs with variable coefficients.…”

Section: Example 2 Consider the Variable Coefficients Linear Didaesmentioning

confidence: 99%

“…The neural networks for solving differential equations can be divided into shallow neural networks (SNNs) and deep neural networks (DNNs). The more popular types of SNNs are functional link neural network models [28,29] and radial basis function neural networks [30,31], and the DNNs are the Deep Ritz Method [32], the physicsinformed neural networks [33][34][35][36][37] and the deep ReLU neural networks [38,39]. The SNNs are relatively fast in training, but they also have their limitations, that is the limitation of their ability to simulate complex functions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chebyshev Neural Network Method for Solving Delay-Integro-Differential-Algebraic Equations Based on Variable Transformation

Xing

Liu

et al. 2023

Preprint

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In this paper, a single hidden layer Chebyshev neural network based on extreme learning machine is proposed to solve linear and nonlinear delay-integro-differential-algebraic equations. Since the equations contain both delay and integral terms, which bring many difficulties to the numerical solution. This paper adopts a segmental solution to overcome the difficulties caused by the delay term and constructs a Chebyshev neural network, which can directly calculate the integral term through the Chebyshev polynomials. For linear delay-integral-differential-algebraic equations, we first segment the interval according to the delay term, construct a single hidden layer Chebyshev neural network, and combine the extreme learning machine optimization algorithm to obtain the optimal solution of each segment in turn, in which the optimal solution of the previous segment is used as the initial condition of the subsequent segment. For the nonlinear delay-integral-differential-algebraic equations, this paper first transforms the nonlinear equation into a linear equation using the variable transformation method, and then we simulate them using the same method. Numerical experiments show that the single hidden layer Chebyshev neural network based on the extreme learning machine can solve the linear model with high accuracy, and it is feasible and efficient to convert the nonlinear model into a linear model by using the variable transformation method for simulation.

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“…The true solution is (29), the delay term τ = 1. Similarly, we divide the interval [0, 3] into three segments [0, 1], [1,2] and [2,3] to solve.…”

Section: Example 2 Consider the Variable Coefficients Linear Didaesmentioning

confidence: 99%

Section: Example 2 Consider the Variable Coefficients Linear Didaesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chebyshev Neural Network Method for Solving Delay-Integro-Differential-Algebraic Equations Based on Variable Transformation

Xing

Liu

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

A neural network approach for solving nonlinear differential equations of Lane–Emden type

Parand,

Aghaei,

Kiani

et al. 2023

Engineering with Computers

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Connectionist Learning Models for Application Problems Involving Differential and Integral Equations

Cited by 2 publications

References 35 publications

Chebyshev Neural Network Method for Solving Delay-Integro-Differential-Algebraic Equations Based on Variable Transformation

Chebyshev Neural Network Method for Solving Delay-Integro-Differential-Algebraic Equations Based on Variable Transformation

A neural network approach for solving nonlinear differential equations of Lane–Emden type

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