Solving two-dimensional linear partial differential equations based on Chebyshev neural network with extreme learning machine algorithm

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Min Liu ◽  
Muzhou Hou ◽  
Juan Wang ◽  
Yangjin Cheng
Keyword(s):  
Neural Network ◽  
Partial Differential Equations ◽  
Extreme Learning Machine ◽  
Two Dimensional ◽  
Content Type ◽  
Linear Partial Differential Equations ◽  
Chebyshev Neural Network ◽  
Learning Machine ◽  
Hidden Layer ◽  
Linear Pdes

Purpose This paper aims to develop a novel algorithm and apply it to solve two-dimensional linear partial differential equations (PDEs). The proposed method is based on Chebyshev neural network and extreme learning machine (ELM) called Chebyshev extreme learning machine (Ch-ELM) method. Design/methodology/approach The network used in the proposed method is a single hidden layer feedforward neural network. The Kronecker product of two Chebyshev polynomials is used as basis function. The weights from the input layer to the hidden layer are fixed value 1. The weights from the hidden layer to the output layer can be obtained by using ELM algorithm to solve the linear equations established by PDEs and its definite conditions. Findings To verify the effectiveness of the proposed method, two-dimensional linear PDEs are selected and its numerical solutions are obtained by using the proposed method. The effectiveness of the proposed method is illustrated by comparing with the analytical solutions, and its superiority is illustrated by comparing with other existing algorithms. Originality/value Ch-ELM algorithm for solving two-dimensional linear PDEs is proposed. The algorithm has fast execution speed and high numerical accuracy.

A normal equation-based extreme learning machine for solving linear partial differential equations

2021 ◽  
pp. 1-12
Author(s):  
Vikas Dwivedi ◽  
Balaji Srinivasan
Keyword(s):  
Neural Network ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Extreme Learning Machine ◽  
Normal Equation ◽  
Partial Differential ◽  
Normal Equations ◽  
Linear Partial Differential Equations ◽  
Learning Machine ◽  
Complicated Geometries

Abstract This paper develops an extreme learning machine for solving linear partial differential equations (PDE) by extending the normal equations approach for linear regression. The normal equations method is typically used when the amount of available data is small. In PDEs, the only available ground truths are the boundary and initial conditions (BC and IC). We use the physics-based cost function used in state-of-the-art deep neural network-based PDE solvers called physics informed neural network (PINN) to compensate for the small data. However, unlike PINN, we derive the normal equations for PDEs and directly solve them to compute the network parameters. We demonstrate our method's feasibility and efficiency by solving several problems like function approximation, solving ordinary differential equations (ODEs), steady and unsteady PDEs on regular and complicated geometries. We also highlight our method's limitation in capturing sharp gradients and propose its domain distributed version to overcome this issue. We show that this approach is much faster than traditional gradient descent-based approaches and offers an alternative to conventional numerical methods in solving PDEs in complicated geometries.

scholarly journals One-Class Classification with Extreme Learning Machine

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Qian Leng ◽  
Honggang Qi ◽  
Jun Miao ◽  
Wentao Zhu ◽  
Guiping Su
Keyword(s):  
Neural Network ◽  
Extreme Learning Machine ◽  
Classification Problem ◽  
Traditional Learning ◽  
Learning Speed ◽  
One Class Classifier ◽  
Learning Machine ◽  
Hidden Layer ◽  
One Class Classification ◽  
Network Approaches

One-class classification problem has been investigated thoroughly for past decades. Among one of the most effective neural network approaches for one-class classification, autoencoder has been successfully applied for many applications. However, this classifier relies on traditional learning algorithms such as backpropagation to train the network, which is quite time-consuming. To tackle the slow learning speed in autoencoder neural network, we propose a simple and efficient one-class classifier based on extreme learning machine (ELM). The essence of ELM is that the hidden layer need not be tuned and the output weights can be analytically determined, which leads to much faster learning speed. The experimental evaluation conducted on several real-world benchmarks shows that the ELM based one-class classifier can learn hundreds of times faster than autoencoder and it is competitive over a variety of one-class classification methods.

Prediction of two-dimensional topography of laser cladding based on neural network

2019 ◽  
Vol 33 (01n03) ◽  
pp. 1940034 ◽  
Author(s):  
Li Hongyu ◽  
Chen Hui ◽  
Wu Ying ◽  
Chen Yong ◽  
Yi Wei
Keyword(s):  
Neural Network ◽  
Error Rate ◽  
Back Propagation ◽  
Feedforward Neural Network ◽  
Two Dimensional ◽  
Back Propagation Algorithm ◽  
Cladding Layer ◽  
Propagation Algorithm ◽  
Learning Machine ◽  
Hidden Layer

The two-dimensional morphology of the cladding layer has an important influence on the quality of the cladding layer and the crack tendency. Using the powerful nonlinear processing ability of the single hidden layer feedforward neural network, a prediction model between the cladding technological parameters and the two-dimensional morphology of the cladding layer is established. Taking the cladding parameters as the input and the two-dimensional morphology of the cladding as the output, the experimental data is used to train the network to achieve a high-level mapping of the input and output. On this basis, the algorithm of extreme learning machine is used to optimize the single hidden layer feedforward neural network to overcome the problems of slow convergence speed, more network training parameters and easy local convergence in back-propagation algorithm. The results show that the relationship between the cladding process parameters and the two-dimensional morphology of the cladding layer can be roughly reflected by the back-propagation algorithm. However, the prediction results are not stable and the error rate is between 10% and 40%. The neural network optimized by the extreme learning machine is utilized to get a better prediction result. The error rate is 10–20%.

scholarly journals An Effective Turkey Marble Classification System: Convolutional Neural Network with Genetic Algorithm -Wavelet Kernel - Extreme Learning Machine

2021 ◽  
Vol 38 (4) ◽  
pp. 1229-1235
Author(s):  
Derya Avci ◽  
Eser Sert
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Convolutional Neural Network ◽  
Extreme Learning Machine ◽  
Optical Illusions ◽  
Factors Affecting ◽  
Kernel Extreme Learning Machine ◽  
Learning Machine ◽  
Hidden Layer ◽  
Elm Classifier

Marble is one of the most popular decorative elements. Marble quality varies depending on its vein patterns and color, which are the two most important factors affecting marble quality and class. The manual classification of marbles is likely to lead to various mistakes due to different optical illusions. However, computer vision minimizes these mistakes thanks to artificial intelligence and machine learning. The present study proposes the Convolutional Neural Network- (CNN-) with genetic algorithm- (GA) Wavelet Kernel- (WK-) Extreme Learning Machine (ELM) (CNN–GA-WK-ELM) approach. Using CNN architectures such as AlexNet, VGG-19, SqueezeNet, and ResNet-50, the proposed approach obtained 4 different feature vectors from 10 different marble images. Later, Genetic Algorithm (GA) was used to optimize adjustable parameters, i.e. k, 1, and m, and hidden layer neuron number in Wavelet Kernel (WK) – Extreme Learning Machine (ELM) and to increase the performance of ELM. Finally, 4 different feature vector parameters were optimized and classified using the WK-ELM classifier. The proposed CNN–GA-WK-ELM yielded an accuracy rate of 98.20%, 96.40%, 96.20%, and 95.60% using AlexNet, SequeezeNet, VGG-19, and ResNet-50, respectively.

scholarly journals Toward deep neural networks: Mirror extreme learning machines for pattern classification

Filomat ◽  
2020 ◽  
Vol 34 (15) ◽  
pp. 4985-4996
Author(s):  
Bolin Liao ◽  
Chuan Ma ◽  
Meiling Liao ◽  
Shuai Li ◽  
Zhiguan Huang
Keyword(s):  
Neural Network ◽  
Extreme Learning Machine ◽  
Pattern Classification ◽  
Simple Structure ◽  
Layer Structure ◽  
Feed Forward Neural Network ◽  
Learning Machines ◽  
S Parameter ◽  
Learning Machine ◽  
Hidden Layer

In this paper, a novel type of feed-forward neural network with a simple structure is proposed and investigated for pattern classification. Because the novel type of forward neural network?s parameter setting is mirrored with those of the Extreme Learning Machine (ELM), it is termed the mirror extreme learning machine (MELM). For the MELM, the input weights are determined by the pseudoinverse method analytically, while the output weights are generated randomly, which are completely different from the conventional ELM. Besides, a growing method is adopted to obtain the optimal hidden-layer structure. Finally, to evaluate the performance of the proposed MELM, abundant comparative experiments based on different real-world classification datasets are performed. Experimental results validate the high classification accuracy and good generalization performance of the proposed neural network with a simple structure in pattern classification.

Extreme Learning Machine for Fault Diagnosis of Rotating Machinery

2014 ◽  
Vol 960-961 ◽  
pp. 1400-1403 ◽  
Author(s):  
Rui Yu ◽  
Rui Xiang ◽  
Shi Wei Yao
Keyword(s):  
Neural Network ◽  
Power Spectrum ◽  
Extreme Learning Machine ◽  
Probabilistic Neural Network ◽  
Wavelet Packet ◽  
Noise Signal ◽  
Rotating Machinery ◽  
Machine Method ◽  
Learning Machine ◽  
Hidden Layer

The authors present extreme learning machine (ELM) as a novel mechanism for diagnosing the faults of rotating machinery, which is reflected from the power spectrum of the vibration signals. Extreme learning machine was originally developed for the single-hidden layer feedforward neural network (SLFN) and then extended to the generalized SLFN. We obtained the fault feature table of rotating machinery by wavelet packet analysis of the power spectrum, then trained and diagnosed the fault feature table with extreme learning machine. Diagnostic results show that the extreme learning machine method achieves higher diagnostic accuracy than the probabilistic neural network (PNN) method, exhibiting superior diagnostic performance. In addition, the diagnosis of fault feature table adding noise signal indicates the extreme learning machine method provides satisfactory generalization performance.

Comparison of the Extreme Learning Machine with the BP Neural Network for Short-Term Prediction of Wind Power

2012 ◽  
Vol 608-609 ◽  
pp. 564-568 ◽  
Author(s):  
Yi Hui Zhang ◽  
He Wang ◽  
Zhi Jian Hu ◽  
Meng Lin Zhang ◽  
Xiao Lu Gong ◽  
...  
Keyword(s):  
Neural Network ◽  
Wind Power ◽  
Extreme Learning Machine ◽  
Bp Neural Network ◽  
Learning Algorithm ◽  
Power Prediction ◽  
Feed Forward Neural Network ◽  
Wind Power Prediction ◽  
Learning Machine ◽  
Hidden Layer

Extreme learning machine (ELM) is a new and effective single-hidden layer feed forward neural network learning algorithm. Extreme learning machine only needs to set the number of hidden layer nodes of the network, and there is no need to adjust the neural network input weights and the hidden units bias, and it generates the only optimum solution, so it has the advantage of fast learning and good generalization ability. And the back propagation (BP) neural network is the most maturely applied. This paper has introduced the extreme learning machine into the wind power prediction. By comparing the wind power prediction method using the BP neural network. Study shows that the extreme learning machine has better prediction accuracy and shorter model training time.

Predicting Surface Roughness in Turning Operation Using Extreme Learning Machine

2014 ◽  
Vol 554 ◽  
pp. 431-435 ◽  
Author(s):  
Ahmad Nooraziah ◽  
V. Janahiraman Tiagrajah
Keyword(s):  
Neural Network ◽  
Surface Roughness ◽  
Extreme Learning Machine ◽  
Cutting Parameters ◽  
Feedforward Neural Network ◽  
Support Vector ◽  
Satisfactory Solution ◽  
Modeling Techniques ◽  
Learning Machine ◽  
Hidden Layer

Prediction model allows the machinist to determine the values of the cutting performance before machining. According to literature, various modeling techniques have been investigated and applied to predict the cutting parameters. Recently, Extreme Learning Machine (ELM) has been introduced as the alternative to overcome the limitation from the previous methods. ELM has similar structure as single hidden layer feedforward neural network with analytically to determine output weight. By comparing to Response Surface Methodology, Support Vector Machine and Neural Network, this paper proposed the prediction of surface roughness using ELM method. The result indicates that ELM can yield satisfactory solution for predicting surface roughness in term of training speed and parameter selection.

scholarly journals Learning of a single-hidden layer feedforward neural network using an optimized extreme learning machine

2014 ◽  
Vol 129 ◽  
pp. 428-436 ◽  
Author(s):  
Tiago Matias ◽  
Francisco Souza ◽  
Rui Araújo ◽  
Carlos Henggeler Antunes
Keyword(s):  
Neural Network ◽  
Extreme Learning Machine ◽  
Feedforward Neural Network ◽  
Learning Machine ◽  
Hidden Layer
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