Design of artificial neural network models optimized with sequential quadratic programming to study the dynamics of nonlinear Troesch’s problem arising in plasma physics

In this study, a computational intelligence technique based on three different designs of artificial neural networks (ANNs) is presented to solve the nonlinear Troesch’s boundary value problem arising in plasma physics. The structure of three ANN models is formulated by incorporating log-sigmoid (AN...

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Veröffentlicht in:Neural computing & applications Jg. 29; H. 6; S. 83 - 109
Hauptverfasser: Raja, Muhammad Asif Zahoor, Shah, Fiaz Hussain, Tariq, Muhammad, Ahmad, Iftikhar, Ahmad, Siraj ul Islam
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Springer London 01.03.2018
Springer Nature B.V
Schlagworte:
Artificial Intelligence
Artificial neural networks
Boundary value problems
Computational Biology/Bioinformatics
Computational Science and Engineering
Computer Science
Data Mining and Knowledge Discovery
Design optimization
Error functions
Image Processing and Computer Vision
Kernel functions
Learning theory
Mathematical models
Model accuracy
Neural networks
Original Article
Parameters
Performance indices
Plasma physics
Plasmas (physics)
Probability and Statistics in Computer Science
Quadratic programming
Statistical analysis
Troesch’s problem
Sequential quadratic programming
Stochastic solvers
Artificial neural networks
Activation functions
ISSN:0941-0643, 1433-3058
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Beschreibung
Zusammenfassung:In this study, a computational intelligence technique based on three different designs of artificial neural networks (ANNs) is presented to solve the nonlinear Troesch’s boundary value problem arising in plasma physics. The structure of three ANN models is formulated by incorporating log-sigmoid (ANN-LS), radial-base (ANN-RB) and tan-sigmoid (ANN-TS) kernel functions in the hidden layers. Mathematical modeling of the problem is constructed for all three feed-forward ANN models by defining an error function in an unsupervised manner. Sequential quadratic programming method is employed for the learning of unknown parameters for all three ANN-LS, ANN-RB and ANN-TS schemes. The proposed models are applied to solve variants of Troesch’s problems by taking the small and large values of critical parameter in the system. A comparison of the proposed solution obtained from these models has been made with the standard numerical results of Adams method. The accuracy and convergence of the proposed models are investigated through results of statistical analysis in terms of performance indices based on the mean absolute deviation, root-mean-square error and variance account for.
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ISSN:0941-0643
1433-3058
DOI:10.1007/s00521-016-2530-2