Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations

Yang, Yunlei; Hou, Muzhou; Sun, Hongli; Zhang, Tianle; Weng, Futian; Luo, Jianshu

doi:10.1007/s00500-019-03944-1

Cited by 40 publications

(26 citation statements)

References 46 publications

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“…It is proven that the ELM's origin is based on Random Vector Functional Link (RVLF) [51,52], leading to the ultra-fast learning and outstanding generalization capability [53,54]. Literature survey shows that ELM has been broadly utilized in many engineering applications [55][56][57]. Although various kinds of ELMs are now accessible for image detection and classification tasks, it confronts serious issues such as the need for many hidden nodes for better generalization and Cite as: Chao Wu, Mohammad Khishe, Mokhtar Mohammadi, Sarkhel H. Taher Karim & Tarik A. Rashid (2021).…”

Section: Introductionmentioning

confidence: 99%

RETRACTED ARTICLE: Evolving deep convolutional neutral network by hybrid sine–cosine and extreme learning machine for real-time COVID19 diagnosis from X-ray images

Khishe²,

Mohammadi

et al. 2021

Soft Comput

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The COVID19 pandemic globally and significantly has affected the life and health of many communities. The early detection of infected patients is effective in fighting COVID19. Using radiology (X-Ray) images is, perhaps, the fastest way to diagnose the patients. Thereby, deep Convolutional Neural Networks (CNNs) can be considered as applicable tools to diagnose COVID19 positive cases. Due to the complicated architecture of a deep CNN, its real-time training and testing become a challenging problem. This paper proposes using the Extreme Learning Machine (ELM) instead of the last fully connected layer to address this deficiency. However, the parameters’ stochastic tuning of ELM’s supervised section causes the final model unreliability. Therefore, to cope with this problem and maintain network reliability, the sine–cosine algorithm was utilized to tune the ELM’s parameters. The designed network is then benchmarked on the COVID-Xray-5k dataset, and the results are verified by a comparative study with canonical deep CNN, ELM optimized by cuckoo search, ELM optimized by genetic algorithm, and ELM optimized by whale optimization algorithm. The proposed approach outperforms comparative benchmarks with a final accuracy of 98.83% on the COVID-Xray-5k dataset, leading to a relative error reduction of 2.33% compared to a canonical deep CNN. Even more critical, the designed network’s training time is only 0.9421 ms and the overall detection test time for 3100 images is 2.721 s.

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Section: Introductionmentioning

confidence: 99%

RETRACTED ARTICLE: Evolving deep convolutional neutral network by hybrid sine–cosine and extreme learning machine for real-time COVID19 diagnosis from X-ray images

Khishe²,

Mohammadi

et al. 2021

Soft Comput

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show abstract

“…Suppose that the approximate solution to (27) is y = ω T φ(x) + b, the original optimal problem is described as follows: min ω,b,e i J(ω, e) = 1 2 ω T ω + 1 2 γ e T e (28) subject to…”

Section: Linear Ordinary Differential Equations For Multi-point Boundmentioning

confidence: 99%

“…Neural network, which is one of machine intelligence techniques, has universal function approximation capabilities [20][21][22], and the solution obtained from the neural network is differentiable and in closed analytic form. Neural network has been widely used for solving ordinary differential equations [23,24], partial differential equations [25][26][27], fractional differential equations [28][29][30], and integro-differential equations [31,32]. Chakraverty and Mall [33] analyzed a regression-based neural network algorithm to solve two-point boundary value problems of fourth-order linear ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

The LS-SVM algorithms for boundary value problems of high-order ordinary differential equations

Yin

et al. 2019

Adv Differ Equ

Self Cite

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This paper introduces the improved LS-SVM algorithms for solving two-point and multi-point boundary value problems of high-order linear and nonlinear ordinary differential equations. To demonstrate the reliability and powerfulness of the improved LS-SVM algorithms, some numerical experiments for third-order, fourth-order linear and nonlinear ordinary differential equations with two-point and multi-point boundary conditions are performed. The idea can be extended to other complicated ordinary differential equations.

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“…Under certain conditions, the alternating minimum algorithm used is convergent [7]. Yang et al proposed an image segmentation algorithm based on the global positive radial basis function by combining the method of global positive radial basis function and partial differential equation [8]. This algorithm integrates the global positive radial basis function difference method into the level set function image segmentation model.…”

Section: Introductionmentioning

confidence: 99%

Application of Image Segmentation Algorithm Based on Partial Differential Equation in Legal Case Text Classification

Sun

2021

Advances in Mathematical Physics

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As a means of regulating people’s code of conduct, law has a close relationship with text, and text data has been growing exponentially. Managing and classifying huge text data have become a huge challenge. The PDES image segmentation algorithm is an effective natural language processing method for text classification management. Based on the study of image segmentation algorithm and legal case text classification theory, an image segmentation model based on partial differential equation is proposed, in which diffusion indirectly acts on level set function through auxiliary function. The software architecture of image segmentation algorithm text classification system is proposed by using computer technology and three-layer architecture model, which can improve the classification ability of text classification algorithm. The validity of pDE image segmentation model is verified by experiments. The experimental results show that the model completes the legal case text classification, the performance of each functional module of the legal case text classification system is good, and the efficiency and quality of the legal case text classification are improved.

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Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations

Cited by 40 publications

References 46 publications

RETRACTED ARTICLE: Evolving deep convolutional neutral network by hybrid sine–cosine and extreme learning machine for real-time COVID19 diagnosis from X-ray images

RETRACTED ARTICLE: Evolving deep convolutional neutral network by hybrid sine–cosine and extreme learning machine for real-time COVID19 diagnosis from X-ray images

The LS-SVM algorithms for boundary value problems of high-order ordinary differential equations

Application of Image Segmentation Algorithm Based on Partial Differential Equation in Legal Case Text Classification

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