Neural Network Method for Solving Time-Fractional Telegraph Equation

Ibrahim, Wubshet; Bijiga, Lelisa Kebena

doi:10.1155/2021/7167801

Cited by 6 publications

(3 citation statements)

References 26 publications

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“…The HET efficient neural network can solve the Transformer's problems to increase its efficiency in accomplishing downstream tasks [19]. The structure of the HET network is shown in Fig.…”

Section: Het Neural Networkmentioning

confidence: 99%

English Translation Stylistic Features and Syntax Translation with Application of Knowledge Mapping

Zhang

2023

Applied Mathematics and Nonlinear Sciences

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Aiming at the problems of excessive instantiation complexity, poor interpretability and low generalization ability of knowledge reasoning techniques, this paper unites inductive logic programming ILP with HET neural network to construct a hybrid logic rule and neural network knowledge graph reasoning model - HETIL model. The ILP is utilized to quantify the first-order logic rules, and the multi-layer rule space is constructed by arranging and combining the rules through logic symbols. The rules are instantiated and fed into the HET network, and the attention coefficients aggregate the node features to complete the end-to-end training and generate the rule learning model. Finally, the validity of the model is verified by machine translation experiments, and the results show that the accuracy of the HETIL model in syntactic structure types is more than 0.8 overall. The accuracy in terms of phrase structure reaches 0.879. The average BLEU value of the HETIL model can reach 29.24, which is 1.51 BLEU points higher than the benchmark model. Therefore, the effect of English translation by applying a knowledge graph is better than traditional machine translation.

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“…The HET efficient neural network can solve the Transformer's problems to increase its efficiency in accomplishing downstream tasks [19]. The structure of the HET network is shown in Fig.…”

Section: Het Neural Networkmentioning

confidence: 99%

English Translation Stylistic Features and Syntax Translation with Application of Knowledge Mapping

Zhang

2023

Applied Mathematics and Nonlinear Sciences

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“…[ 9 ] designed a Bayesian regularization approach to solve the fractional Layla and Majnun System and solved it accurately [ 10 ]. developed the Gudermannian neural network for solving the nonlinear multi-Pantograph delay differential equation [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

Integrating freelance models with fractional derivatives, and artificial neural networks: A comprehensive approach to advanced computation

Khan,

Majeed,

Khalid

2024

Heliyon

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“…Since there is not an analytical solution for this system, we will propose an artificial neural network (ANN) for solving the problem (1)- (2). Many scholars used ANN to obtain the numerical solutions of the problem in fractional calculus [23]. One of the main advantages of ANN is that we achieved the solution in an analytical form.…”

Section: Introductionmentioning

confidence: 99%

A novel lagrange functional link neural network for solving variable-order fractional time-varying delay differential equations: a comparison with multilayer perceptron neural networks

2023

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In this paper, a new functional link neural network based on Lagrange polynomials is introduced. Due to the well-known efficiency of Lagrange polynomials for solving different problems in fractional calculus, these functions are considered as the neuro-solutions for a class of nonlinear variable-order fractional time-varying delay differential equations. Compared with the other kinds of neural networks such as multilayer perceptron, the suggested functional link neural network shows more satisfactory results. Since the order value of derivative and delay are not constant, it is crucial to choose an appropriate activation function for solving these problems.Then, the effect of some common important activation functions on the numerical simulations is studied. The results for several examples are examined that confirm the performance of the proposed functional neural network.

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Neural Network Method for Solving Time-Fractional Telegraph Equation

Cited by 6 publications

References 26 publications

English Translation Stylistic Features and Syntax Translation with Application of Knowledge Mapping

English Translation Stylistic Features and Syntax Translation with Application of Knowledge Mapping

Integrating freelance models with fractional derivatives, and artificial neural networks: A comprehensive approach to advanced computation

A novel lagrange functional link neural network for solving variable-order fractional time-varying delay differential equations: a comparison with multilayer perceptron neural networks

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