scholarly journals Comparison of Artificial Neural Network Architecture in Solving Ordinary Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Susmita Mall ◽  
S. Chakraverty
Keyword(s):  
Neural Network ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Network Architecture ◽  
Initial Conditions ◽  
Error Function ◽  
Back Propagation ◽  
Feed Forward Neural Network ◽  
Error Back Propagation ◽  
Hidden Layer

This paper investigates the solution of Ordinary Differential Equations (ODEs) with initial conditions using Regression Based Algorithm (RBA) and compares the results with arbitrary- and regression-based initial weights for different numbers of nodes in hidden layer. Here, we have used feed forward neural network and error back propagation method for minimizing the error function and for the modification of the parameters (weights and biases). Initial weights are taken as combination of random as well as by the proposed regression based model. We present the method for solving a variety of problems and the results are compared. Here, the number of nodes in hidden layer has been fixed according to the degree of polynomial in the regression fitting. For this, the input and output data are fitted first with various degree polynomials using regression analysis and the coefficients involved are taken as initial weights to start with the neural training. Fixing of the hidden nodes depends upon the degree of the polynomial. For the example problems, the analytical results have been compared with neural results with arbitrary and regression based weights with four, five, and six nodes in hidden layer and are found to be in good agreement.

scholarly journals Artificial Neural Network Approach for Solving Fuzzy Fractional order initial value problems under H-differentiability

2020 ◽  
Author(s):  
Somayeh Ezadi ◽  
Tofigh Allahviranloo
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Initial Conditions ◽  
Error Function ◽  
Back Propagation ◽  
Back Propagation Algorithm ◽  
Neural Network Approach ◽  
Error Back Propagation ◽  
Artificial Neural ◽  
Artificial Neural Network Ann

This paper aims to solve the celebrated Fuzzy Fractional Differential Equations (FFDE) using an Artificial Neural Network (ANN) technique. Compared to the integer order differential equation, the proposed FFDE can better describe several real application problems of various physical systems. To accomplish the aforementioned aim, the error back propagation algorithm and a multi-layer feed forward neural architecture are utilized using the unsupervised learning in order to minimize the error function as well as the modification of the parameters such as weights and biases. By combining the initial conditions with the ANN, output provides an appropriate approximate solution of the proposed FFDE. Then, two illustrative examples are solved to confirm the applicability of the concept as well as to demonstrate both the precision and effectiveness of the developed method. By comparing with some traditional methods, the obtained results reveals a close match that confirms both accuracy and correctness of the proposed method.

Prediction of geomagnetic storms from solar wind data with the use of a neural network

1994 ◽  
Vol 12 (1) ◽  
pp. 19-24 ◽  
Author(s):  
H. Lundstedt ◽  
P. Wintoft
Keyword(s):  
Neural Network ◽  
Solar Wind ◽  
Geomagnetic Storms ◽  
Activity Index ◽  
Back Propagation ◽  
Recovery Phase ◽  
Feed Forward Neural Network ◽  
Error Back Propagation ◽  
Hidden Layer ◽  
Propagation Network

Abstract. An artificial feed-forward neural network with one hidden layer and error back-propagation learning is used to predict the geomagnetic activity index (Dst) one hour in advance. The Bz-component and ΣBz, the density, and the velocity of the solar wind are used as input to the network. The network is trained on data covering a total of 8700 h, extracted from the 25-year period from 1963 to 1987, taken from the NSSDC data base. The performance of the network is examined with test data, not included in the training set, which covers 386 h and includes four different storms. Whilst the network predicts the initial and main phase well, the recovery phase is not modelled correctly, implying that a single hidden layer error back-propagation network is not enough, if the measured Dst is not available instantaneously. The performance of the network is independent of whether the raw parameters are used, or the electric field and square root of the dynamical pressure.

ARTIFICIAL NEURAL NETWORK (ANN)-BASED PREDICTIVE TOOL FOR ESTIMATING LIGHTNING DAMAGE IN COMPOSITES

2021 ◽  
Author(s):  
DEVIN NIELSEN ◽  
TYLER LOTT ◽  
SOM DUTTA ◽  
JUHYEONG LEE
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Network Architecture ◽  
Back Propagation ◽  
Training Dataset ◽  
Predictive Tool ◽  
Ann Models ◽  
Artificial Neural ◽  
Artificial Neural Network Ann ◽  
Hidden Layer

In this study, three artificial neural network (ANN) models are developed with back propagation (BP) optimization algorithms to predict various lightning damage modes in carbon/epoxy laminates. The proposed ANN models use three input variables associated with lightning waveform parameters (i.e., the peak current amplitude, rising time, and decaying time) to predict fiber damage, matrix damage, and through-thickness damage in the composites. The data used for training and testing the networks was actual lightning damage data collected from peer-reviewed published literature. Various BP training algorithms and network architecture configurations (i.e., data splitting, the number of neurons in a hidden layer, and the number of hidden layers) have been tested to improve the performance of the neural networks. Among the various BP algorithms considered, the Bayesian regularization back propagation (BRBP) showed the overall best performance in lightning damage prediction. When using the BRBP algorithm, as expected, the greater the fraction of the collected data that is allocated to the training dataset, the better the network is trained. In addition, the optimal ANN architecture was found to have a single hidden layer with 20 neurons. The ANN models proposed in this work may prove useful in preliminary assessments of lightning damage and reduce the number of expensive experimental lightning tests.

Prediction of Yarn Quality Based on BP Neural Network

2011 ◽  
Vol 331 ◽  
pp. 449-453
Author(s):  
Jing Yuan ◽  
Ying Lin Li ◽  
Su Ying Chen
Keyword(s):  
Neural Network ◽  
Mathematical Models ◽  
Network Architecture ◽  
Raw Materials ◽  
Nonlinear Approximation ◽  
Back Propagation ◽  
Back Propagation Neural Network ◽  
Yarn Quality ◽  
Spinning Process ◽  
Hidden Layer

As the quality of yarn and the fiber indicators are nonlinear relationship, the traditional mathematical models or empirical formula has been unable to accurately resolve the problem. In view of artificial neural networks do not need to build accurate mathematical models, applicable to solving the problem of yarn quality prediction. In this paper, good nonlinear approximation ability of BP (Back Propagation) neural network be used, the use of neural network toolbox of MATLAB functions for modeling, good results was obtained. Prediction model set a hidden layer, using three-tier network architecture, and take the input layer 4 nodes, hidden layer 8 nodes and output layer 2 nodes. According to forecast results, can ensure the yarn quality effectively, use of raw materials rationally, to achieve optimal distribution of cotton. Meanwhile, the spinning process design can also be provided validation, for the development of new products to provide a theoretical basis.

scholarly journals Estimation of Waste Mobile Phones in the Philippines using Neural Networks

2018 ◽  
Vol 20 (4) ◽  
pp. 767-772
Keyword(s):  
Neural Network ◽  
Mobile Phone ◽  
Mobile Phones ◽  
Network Architecture ◽  
The Philippines ◽  
Strategy Formulation ◽  
Feed Forward Neural Network ◽  
The Neural Network ◽  
Mobile Industry ◽  
Hidden Layer

<p>Waste mobile phone is one of the subgroups of e-waste which is defined as discarded electronic products in the Philippine context. This study estimated current and projected quantities of waste mobile phones in the country using feed forward neural network. The neural network architecture used had three layers: (i) input layer, (ii) hidden layer, and (iii) output layer. Seven input factors were fed to the network: (i) population, (ii) literacy rate, (iii) mobile connections, (iv) mobile subscribers, (v) gross domestic product (GDP), (vi) GDP per capita, and (vii) US dollar to Philippine peso exchange rate. These input factors were selected based on the criteria provided in the study by the Groupe Spéciale Mobile Association (GSMA) Intelligence in 2015 on why the Philippines is an innovation hub in mobile industry and the availability of data from the sources. The structure was designed with five hidden layers which consisted of (i) six neurons for layer 1, (ii) five neurons for layer 2, (iii) four neurons for layer 3, (iv) three neurons for layer 4, and (v) two neurons for layer 5. The neural network was designed to initially calculate the sales of mobile phones before estimating waste mobile phone generation. Visual Gene Developer 1.7 Software was used which achieved a sum of squared error of 0.00001. Estimated values were found to be in good agreement with a calculated accuracy of 99%. This study can be used by policy makers as basis for strategy formulation and as guideline and baseline data for establishing a proper management system. Neural network performed better than the traditional linear extrapolation method for forecasting of data.</p>

Selecting the architecture of a class of back-propagation neural networks used as approximators

1997 ◽  
Vol 11 (1) ◽  
pp. 33-44 ◽  
Author(s):  
William C. Carpenter ◽  
Margery E. Hoffman
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Back Propagation ◽  
Region Of Interest ◽  
Input Output ◽  
Advantages And Disadvantages ◽  
Back Propagation Neural Networks ◽  
Input Layer ◽  
Hidden Layer

AbstractThis paper examines the architecture of back-propagation neural networks used as approximators by addressing the interrelationship between the number of training pairs and the number of input, output, and hidden layer nodes required for a good approximation. It concentrates on nets with an input layer, one hidden layer, and one output layer. It shows that many of the currently proposed schemes for selecting network architecture for such nets are deficient. It demonstrates in numerous examples that overdetermined neural networks tend to give good approximations over a region of interest, while underdetermined networks give approximations which can satisfy the training pairs but may give poor approximations over that region of interest. A scheme is presented that adjusts the number of hidden layer nodes in a neural network so as to give an overdetermined approximation. The advantages and disadvantages of using multiple output nodes are discussed. Guidelines for selecting the number of output nodes are presented.

Multiple Faults Detection of Gas Turbine by MLP Neural Network

2009 ◽  
Author(s):  
Gustavo R. Matuck ◽  
Joa˜o Roberto Barbosa ◽  
Cleverson Bringhenti ◽  
Isaias Lima
Keyword(s):  
Neural Network ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Back Propagation ◽  
Optimization Techniques ◽  
Multiple Faults ◽  
Error Back Propagation ◽  
Artificial Neural ◽  
Hidden Layer ◽  
Simulator Program

This paper describes a procedure to measure the performance of detection and isolation of multiple faults in gas turbines using artificial neural network and optimization techniques. It is on a particular form of artificial neural networks, the traditional multi-layer perceptron (MLP). Error back-propagation and different activation functions are used. The main goal is to recognize single, double and triple faults in a turboshaft engine, whose performance data were output from a gas turbine simulator program, tuned to represent the engine running at an existing power station. MLP network is a nonlinear interpolation function usually made of input layer, hidden-layer and output-layer, with different neuronal units, but in this work, only one hidden-layer was used. Weights were altered by error back-propagation from the initial values established from a seed fixed between 0 and 1. The activation function in the MLP algorithm is the sigmoid function. The best moment to stop the training process and avoid the over fitting problem was chosen by cross-validation. Optimization of convergence error was achieved using the momentum criteria and reducing the oscillation problem in all nets trained. Several configurations of the neural network have been compared and evaluated, using several noise graduations incorporated to the data, aiming at finding the network most suitable to detect and isolate multiple faults in gas turbines. Based on the results obtained it is inferred that the procedure reported herein may be applied to actual systems in order to assist in maintenance programs, at least.

scholarly journals Neural Network Identifiability for a Family of Sigmoidal Nonlinearities

2021 ◽  
Author(s):  
Verner Vlačić ◽  
Helmut Bölcskei
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Uniform Norm ◽  
Feed Forward Neural Network ◽  
The Subject ◽  
Hidden Layer ◽  
Arbitrary Precision ◽  
Necessary And Sufficient ◽  
Fully Connected

AbstractThis paper addresses the following question of neural network identifiability: Does the input–output map realized by a feed-forward neural network with respect to a given nonlinearity uniquely specify the network architecture, weights, and biases? The existing literature on the subject (Sussman in Neural Netw 5(4):589–593, 1992; Albertini et al. in Artificial neural networks for speech and vision, 1993; Fefferman in Rev Mat Iberoam 10(3):507–555, 1994) suggests that the answer should be yes, up to certain symmetries induced by the nonlinearity, and provided that the networks under consideration satisfy certain “genericity conditions.” The results in Sussman (1992) and Albertini et al. (1993) apply to networks with a single hidden layer and in Fefferman (1994) the networks need to be fully connected. In an effort to answer the identifiability question in greater generality, we derive necessary genericity conditions for the identifiability of neural networks of arbitrary depth and connectivity with an arbitrary nonlinearity. Moreover, we construct a family of nonlinearities for which these genericity conditions are minimal, i.e., both necessary and sufficient. This family is large enough to approximate many commonly encountered nonlinearities to within arbitrary precision in the uniform norm.

scholarly journals Particle Swarm Optimization to Obtain Weights in Neural Network

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Budi Warsito ◽  
Hasbi Yasin ◽  
Alan Prahutama
Keyword(s):  
Neural Network ◽  
Particle Swarm Optimization ◽  
Network Model ◽  
Neural Network Model ◽  
Network Architecture ◽  
Optimization Technique ◽  
Particle Swarm ◽  
Feed Forward Neural Network ◽  
Swarm Optimization ◽  
Hidden Layer

This research discusses the use of a class of heuristic optimization to obtain the weights in neural network model for time series prediction. In this case, Feed Forward Neural Network (FFNN) was chosen as the class of network architecture. The heuristic algorithm determined to obtain the weights in network was Particle Swarm Optimization (PSO). It is a non-gradient optimization technique. This method was used for optimizing the connection weights of network. The lags used as the input were selected based on the strong relationship with the current. The eight architectures were conducted to improve the accuracy of the neural network model. In each architecture, we repeated the running thirty times to get the statistics of mean and variance. The comparison of the performance of various architectures based on the minimum MSE and the stability of the results is presented in this paper. The optimal number of neurons in hidden layer was determined by these criteria. The proposed procedure was applied in air pollution data, i.e. Solid Particulate Matter (SPM). The results showed that the proposed procedure gave promising results in terms of prediction accuracy. A few neurons in hidden layer are strongly recommended in choosing the optimal architecture.

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