An improved optimal trigonometric ELM algorithm for numerical solution to ruin probability of Erlang(2) risk model

Cheng, Yangjin; Hou, Muzhou; Wang, Juan

doi:10.1007/s11042-020-09382-8

Cited by 5 publications

(3 citation statements)

References 60 publications

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“…An ELM is a machine learning method based on a feedforward neural network. Unlike ANNs, the weights of the nodes in the hidden layer of the ELM model are artificially assigned and do not require updating [ 25 ]. QR matrix decomposition is an effective method of solving all eigenvalues of general matrices and is widely used in matrix generalised inverse calculation and least-squares problem solving [ 26 ].…”

Section: Correlation Theorymentioning

confidence: 99%

Drought prediction based on an improved VMD-OS-QR-ELM model

Liu

Wang

et al. 2022

PLoS ONE

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To overcome the low accuracy, poor reliability, and delay in the current drought prediction models, we propose a new extreme learning machine (ELM) based on an improved variational mode decomposition (VMD). The model first redefines the output of the hidden layer of the ELM model with orthogonal triangular matrix decomposition (QR) to construct an orthogonal triangular ELM (QR-ELM), and then introduces an online sequence learning mechanism (OS) into the QR-ELM to construct an online sequence OR-ELM (OS-QR-ELM), which effectively improves the efficiency of the ELM model. The mutual information extension method was then used to extend both ends of the original signal to improve the VMD end effect. Finally, VMD and OS-QR-ELM were combined to construct a drought prediction method based on the VMD-OS-QR-ELM. The reliability and accuracy of the VMD-OS-QR-ELM model were improved by 86.19% and 93.20%, respectively, compared with those of the support vector regression model combined with empirical mode decomposition. Furthermore, the calculation efficiency of the OS-QR-ELM model was increased by 88.65% and 85.32% compared with that of the ELM and QR-ELM models, respectively.

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Section: Correlation Theorymentioning

confidence: 99%

Drought prediction based on an improved VMD-OS-QR-ELM model

Liu

Wang

et al. 2022

PLoS ONE

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“…Hongli et al [36] introduced Bernstein Neural Network algorithm based on ELM and Bernstein polynomial to solve directly first order ODEs, second order ODEs and partial differential equations(PDEs). Yangjin and Yanfei respectively proposed trigonometric neural network algorithm and Legendre Neural Network algorithm for solving the ruin probabilities in the classical risk model and the Erlang(2) risk model [37], [38]. Yinghao [39] proposed a numerical method of the generalized Black-Scholes differential equation using Laguerre neural network.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for initial and boundary value problems of high-order ordinary differential equations using Hermite neural network algorithm with improved extreme learning machine

Weng

Sun

2021

Preprint

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In this paper we put forth Hermite neural network (HNN) algorithm with improved extreme learning machine (IELM) to solve initial/boundary value problems of high-order ordinary differential equation(ODEs) and high-order system of ordinary differential equations (SODEs). The model function was expressed as a sum of two terms, where the first term contains no adjustable parameters but satisfies the initial/boundary conditions, the second term involved a single-layered neural network structure with IELM and Hermite basis functions to be trained. The approximate solution is presented in closed form by means of HNN algorithm, whose parameters are obtained by solving a system of linear equations utilizing IELM, which reduces the complexity of the problem. Numerical results demonstrate that the method is effective and reliable for solving high-order ODEs and high-order SODEs with initial and boundary conditions.Mathematics Subject Classification (2020) 34A30 ; 65D15

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“…Sun et al (2018) introduced Bernstein NN algorithm based on ELM and Bernstein polynomial to solve directly first order ODEs, second order ODEs and PDEs. Yangjin and Yanfei respectively proposed trigonometric NN algorithm and Legendre NN algorithm for solving the ruin probabilities in the classical risk model and the Erlang (2) risk model (Cheng et al, 2020;Lu et al, 2020). Chen et al (2021) proposed a numerical method of the generalized Black-Scholes differential equation using Laguerre NN.…”

mentioning

confidence: 99%

Numerical solution for high-order ordinary differential equations using H-ELM algorithm

Weng

Sun

2022

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PurposeThis paper aims to introduce a novel algorithm to solve initial/boundary value problems of high-order ordinary differential equations (ODEs) and high-order system of ordinary differential equations (SODEs).Design/methodology/approachThe proposed method is based on Hermite polynomials and extreme learning machine (ELM) algorithm. The Hermite polynomials are chosen as basis function of hidden neurons. The approximate solution and its derivatives are expressed by utilizing Hermite network. The model function is designed to automatically meet the initial or boundary conditions. The network parameters are obtained by solving a system of linear equations using the ELM algorithm.FindingsTo demonstrate the effectiveness of the proposed method, a variety of differential equations are selected and their numerical solutions are obtained by utilizing the Hermite extreme learning machine (H-ELM) algorithm. Experiments on the common and random data sets indicate that the H-ELM model achieves much higher accuracy, lower complexity but stronger generalization ability than existed methods. The proposed H-ELM algorithm could be a good tool to solve higher order linear ODEs and higher order linear SODEs.Originality/valueThe H-ELM algorithm is developed for solving higher order linear ODEs and higher order linear SODEs; this method has higher numerical accuracy and stronger superiority compared with other existing methods.

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An improved optimal trigonometric ELM algorithm for numerical solution to ruin probability of Erlang(2) risk model

Cited by 5 publications

References 60 publications

Drought prediction based on an improved VMD-OS-QR-ELM model

Drought prediction based on an improved VMD-OS-QR-ELM model

Numerical solution for initial and boundary value problems of high-order ordinary differential equations using Hermite neural network algorithm with improved extreme learning machine

Numerical solution for high-order ordinary differential equations using H-ELM algorithm

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