Evolutionary heuristic with Gudermannian neural networks for the nonlinear singular models of third kind

2021 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Hafiz Abdul Wahab

Abstract The presented research work articulates a new design of heuristic computing platform with artificial intelligence algorithm by exploitation of modeling with feed-forward Gudermannian neural networks (FFGNN) trained with global search viability of genetic algorithms (GA) hybrid with speedy local convergence ability of sequential quadratic programing (SQP) approach, i.e., FFGNN-GASQP for solving the singular nonlinear third order Emden-Fowler (SNEF) models. The proposed FFGNN-GASQP intelligent computing solver Gudermannian kernel unified in the hidden layer structure of FFGNN systems of differential operators based on the SNEF that are arbitrary connected to represent the error-based merit function. The optimization objective function is performed with hybrid heuristics of GASQP. Three problems of the third order SNEF are used to evaluate the correctness, robustness and effectiveness of the designed FFGNN-GASQP scheme. Statistical assessments of the performance of FFGNN-GASQP are used to validate the consistent accuracy, convergence and stability.

Author(s):  
А.К. Бойцов ◽  
А.А. Логачев ◽  
Х.Г. Мусин

Оценка перспективности использования клонов гибридных пород древесины является одной из актуальных задач для повышения эффективности плантационного лесовыращивания. Одним из перспективных путей решения данной задачи является применение искусственных нейронных сетей (ИНС). Настоящая научная работа является одной из немногих, где применяется ИНС для решения подобных задач в лесном хозяйстве. Для обучения нейронных сетей и определения перспективности использования клонов гибридных пород древесины для плантационного лесовыращивания были взяты биометрические данные клонов гибридной осины 2018 г. В ходе выполнения работы были построены две ИНС, где архитектура первой сети включает входной слой из 3 нейронов, 1 скрытый слой с 6 нейронами и выходной слой из 1 нейрона; архитектура второй сети включает в себя входной слой из 3 нейронов, 2 скрытых слоя по 6 нейронов и выходной слой из 1 нейрона, в которые были загружены нормализованные исходные биометрические данные для обучения определения перспективности использования клонов гибридных пород древесины для плантационного лесовыращивания. По результатам данного исследования была составлена сравнительная характеристика точности ИНС 1 и ИНС 2, которая показала, что ИНС 1 более точная, так как её отклонение на 3,49% меньше ИНС 2. Результаты настоящей работы подтвердили перспективность применения ИНС для оценки использования клонов гибридных пород древесины для плантационного лесовыращивания. По оценке расчётной перспективности ИНС 1 для плантационного лесовыращивания были выявлены клоны гибридных пород древесины VTI, ESCH3, ESCH5. Внедрение ИНС в отрасль лесного хозяйства упрощает оценку результатов биометрических показателей древесины, особенно для начинающих специалистов, что обеспечивает последующую точную оценку перспективности пород древесины. Assessing the prospects of using hybrid wood clones is one of the urgent tasks to improve the efficiency of plantation silviculture. One of the promising ways to solve this problem is the use of artificial neural networks (ANN). This research work is one of the few where ANN are used to solve such problems in forestry. Biometric data from 2018 hybrid aspen clones were taken to train neural networks and determine the potential use of hybrid wood clones for plantation silviculture. During this work, two ANNs were constructed where the architecture of the first network includes an input layer of 3 neurons, 1 hidden layer with 6 neurons and an output layer of 1 neuron, the architecture of the second network includes an input layer of 3 neurons, 2 hidden layers of 6 neurons and an output layer of 1 neuron, into which the normalized input biometric data were loaded for learning to determine the prospective use of hybrid wood species clones for plantation silviculture. Based on the results of this study, a comparison of the accuracy of ANN 1 and ANN 2 was made, which showed that ANN 1 was more accurate because its bias was 3,49% less than ANN 2. The results of this work confirmed the promise of using ANN to evaluate the use of hybrid wood clones for plantation reforestation. According to the evaluation of the calculated promisingness of ANN 1 for plantation silviculture, VTI, ESCH3 and ESCH5 hybrid wood clones were identified. The introduction of ANN in the forestry industry simplifies the evaluation of wood biometric results, especially for beginners, which provides a subsequent accurate assessment of the perspective of wood species.


2021 ◽  
Vol 11 (11) ◽  
pp. 4725
Author(s):  
Kashif Nisar ◽  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Ag. Asri Ag. Ibrahim ◽  
Joel J. P. C. Rodrigues ◽  
...  

In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.


2019 ◽  
Vol 12 (3) ◽  
pp. 156-161 ◽  
Author(s):  
Aman Dureja ◽  
Payal Pahwa

Background: In making the deep neural network, activation functions play an important role. But the choice of activation functions also affects the network in term of optimization and to retrieve the better results. Several activation functions have been introduced in machine learning for many practical applications. But which activation function should use at hidden layer of deep neural networks was not identified. Objective: The primary objective of this analysis was to describe which activation function must be used at hidden layers for deep neural networks to solve complex non-linear problems. Methods: The configuration for this comparative model was used by using the datasets of 2 classes (Cat/Dog). The number of Convolutional layer used in this network was 3 and the pooling layer was also introduced after each layer of CNN layer. The total of the dataset was divided into the two parts. The first 8000 images were mainly used for training the network and the next 2000 images were used for testing the network. Results: The experimental comparison was done by analyzing the network by taking different activation functions on each layer of CNN network. The validation error and accuracy on Cat/Dog dataset were analyzed using activation functions (ReLU, Tanh, Selu, PRelu, Elu) at number of hidden layers. Overall the Relu gave best performance with the validation loss at 25th Epoch 0.3912 and validation accuracy at 25th Epoch 0.8320. Conclusion: It is found that a CNN model with ReLU hidden layers (3 hidden layers here) gives best results and improve overall performance better in term of accuracy and speed. These advantages of ReLU in CNN at number of hidden layers are helpful to effectively and fast retrieval of images from the databases.


Author(s):  
Volodymyr Shymkovych ◽  
Sergii Telenyk ◽  
Petro Kravets

AbstractThis article introduces a method for realizing the Gaussian activation function of radial-basis (RBF) neural networks with their hardware implementation on field-programmable gaits area (FPGAs). The results of modeling of the Gaussian function on FPGA chips of different families have been presented. RBF neural networks of various topologies have been synthesized and investigated. The hardware component implemented by this algorithm is an RBF neural network with four neurons of the latent layer and one neuron with a sigmoid activation function on an FPGA using 16-bit numbers with a fixed point, which took 1193 logic matrix gate (LUTs—LookUpTable). Each hidden layer neuron of the RBF network is designed on an FPGA as a separate computing unit. The speed as a total delay of the combination scheme of the block RBF network was 101.579 ns. The implementation of the Gaussian activation functions of the hidden layer of the RBF network occupies 106 LUTs, and the speed of the Gaussian activation functions is 29.33 ns. The absolute error is ± 0.005. The Spartan 3 family of chips for modeling has been used to get these results. Modeling on chips of other series has been also introduced in the article. RBF neural networks of various topologies have been synthesized and investigated. Hardware implementation of RBF neural networks with such speed allows them to be used in real-time control systems for high-speed objects.


Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 56
Author(s):  
Haoyu Niu ◽  
Jiamin Wei ◽  
YangQuan Chen

Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for single hidden layer feed-forward neural networks, such as Randomized Radial Basis Function (RBF) Networks and Random Vector Functional-link (RVFL), the SCN randomly assigns the input weights and biases of the hidden nodes in a supervisory mechanism. Since the parameters in the hidden layers are randomly generated in uniform distribution, hypothetically, there is optimal randomness. Heavy-tailed distribution has shown optimal randomness in an unknown environment for finding some targets. Therefore, in this research, the authors used heavy-tailed distributions to randomly initialize weights and biases to see if the new SCN models can achieve better performance than the original SCN. Heavy-tailed distributions, such as Lévy distribution, Cauchy distribution, and Weibull distribution, have been used. Since some mixed distributions show heavy-tailed properties, the mixed Gaussian and Laplace distributions were also studied in this research work. Experimental results showed improved performance for SCN with heavy-tailed distributions. For the regression model, SCN-Lévy, SCN-Mixture, SCN-Cauchy, and SCN-Weibull used less hidden nodes to achieve similar performance with SCN. For the classification model, SCN-Mixture, SCN-Lévy, and SCN-Cauchy have higher test accuracy of 91.5%, 91.7% and 92.4%, respectively. Both are higher than the test accuracy of the original SCN.


2021 ◽  
Vol 47 (2) ◽  
pp. 1-29
Author(s):  
Lambert Theisen ◽  
Manuel Torrilhon

We present a mixed finite element solver for the linearized regularized 13-moment equations of non-equilibrium gas dynamics. The Python implementation builds upon the software tools provided by the FEniCS computing platform. We describe a new tensorial approach utilizing the extension capabilities of FEniCS’ Unified Form Language to define required differential operators for tensors above second degree. The presented solver serves as an example for implementing tensorial variational formulations in FEniCS, for which the documentation and literature seem to be very sparse. Using the software abstraction levels provided by the Unified Form Language allows an almost one-to-one correspondence between the underlying mathematics and the resulting source code. Test cases support the correctness of the proposed method using validation with exact solutions. To justify the usage of extended gas flow models, we discuss typical application cases involving rarefaction effects. We provide the documented and validated solver publicly.


Author(s):  
Serkan Kiranyaz ◽  
Junaid Malik ◽  
Habib Ben Abdallah ◽  
Turker Ince ◽  
Alexandros Iosifidis ◽  
...  

AbstractThe recently proposed network model, Operational Neural Networks (ONNs), can generalize the conventional Convolutional Neural Networks (CNNs) that are homogenous only with a linear neuron model. As a heterogenous network model, ONNs are based on a generalized neuron model that can encapsulate any set of non-linear operators to boost diversity and to learn highly complex and multi-modal functions or spaces with minimal network complexity and training data. However, the default search method to find optimal operators in ONNs, the so-called Greedy Iterative Search (GIS) method, usually takes several training sessions to find a single operator set per layer. This is not only computationally demanding, also the network heterogeneity is limited since the same set of operators will then be used for all neurons in each layer. To address this deficiency and exploit a superior level of heterogeneity, in this study the focus is drawn on searching the best-possible operator set(s) for the hidden neurons of the network based on the “Synaptic Plasticity” paradigm that poses the essential learning theory in biological neurons. During training, each operator set in the library can be evaluated by their synaptic plasticity level, ranked from the worst to the best, and an “elite” ONN can then be configured using the top-ranked operator sets found at each hidden layer. Experimental results over highly challenging problems demonstrate that the elite ONNs even with few neurons and layers can achieve a superior learning performance than GIS-based ONNs and as a result, the performance gap over the CNNs further widens.


2016 ◽  
Vol 16 (2) ◽  
pp. 43-50 ◽  
Author(s):  
Samander Ali Malik ◽  
Assad Farooq ◽  
Thomas Gereke ◽  
Chokri Cherif

Abstract The present research work was carried out to develop the prediction models for blended ring spun yarn evenness and tensile parameters using artificial neural networks (ANNs) and multiple linear regression (MLR). Polyester/cotton blend ratio, twist multiplier, back roller hardness and break draft ratio were used as input parameters to predict yarn evenness in terms of CVm% and yarn tensile properties in terms of tenacity and elongation. Feed forward neural networks with Bayesian regularisation support were successfully trained and tested using the available experimental data. The coefficients of determination of ANN and regression models indicate that there is a strong correlation between the measured and predicted yarn characteristics with an acceptable mean absolute error values. The comparative analysis of two modelling techniques shows that the ANNs perform better than the MLR models. The relative importance of input variables was determined using rank analysis through input saliency test on optimised ANN models and standardised coefficients of regression models. These models are suitable for yarn manufacturers and can be used within the investigated knowledge domain.


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