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

• Published in: Neural computing & applications Vol. 29; no. 6; pp. 83 - 109
• Main Authors: Raja, Muhammad Asif Zahoor, Shah, Fiaz Hussain, Tariq, Muhammad, Ahmad, Iftikhar, Ahmad, Siraj ul Islam
• Format: Journal Article
• Language: English
• Published: London Springer London 01.03.2018; Springer Nature B.V
• Subjects: 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
• DOI: 10.1007/s00521-016-2530-2

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.