TY - JOUR
T1 - Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model
AU - Raja, Muhammad Asif Zahoor
AU - Shah, Fiaz Hussain
AU - Syam, Muhammad Ibrahim
N1 - Funding Information:
Acknowledgement The authors would like to express their appreciation to the United Arab Emirates University Research Affairs for the financial support of Grant No. COS/IRG-09/15.
Funding Information:
The authors would like to express their appreciation to the United Arab Emirates University Research Affairs for the financial support of Grant No. COS/IRG-09/15. All the authors of the manuscript declared that there are no conflicts of interest
Publisher Copyright:
© 2017, The Natural Computing Applications Forum.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - In this work, an intelligent computing algorithm is developed for finding the approximate solution of heart model based on nonlinear Van der Pol (VdP)-type second-order ordinary differential equations (ODEs) using feed-forward artificial neural networks (FF-ANNs) optimized with genetic algorithms (GAs) hybrid through interior-point algorithm (IPA). The mathematical modeling of the system is constructed using FF-ANN models by defining an unsupervised error and unknown weights; the networks are tuned globally with GAs, and local refinement of the results is made with IPA. Design scheme is applied to study the VdP heart dynamics model by varying the pulse shape modification factor, damping coefficients and external forcing factor while keeping the fixed value of the ventricular contraction period. The results of the proposed algorithm are compared with reference numerical solutions of Adams method to establish its correctness. Multiple independent runs are performed for the scheme, and results of statistical analyses in terms of mean absolute deviation, root-mean-square error and Nash–Sutcliffe efficiency illustrate its applicability, effectiveness and reliability.
AB - In this work, an intelligent computing algorithm is developed for finding the approximate solution of heart model based on nonlinear Van der Pol (VdP)-type second-order ordinary differential equations (ODEs) using feed-forward artificial neural networks (FF-ANNs) optimized with genetic algorithms (GAs) hybrid through interior-point algorithm (IPA). The mathematical modeling of the system is constructed using FF-ANN models by defining an unsupervised error and unknown weights; the networks are tuned globally with GAs, and local refinement of the results is made with IPA. Design scheme is applied to study the VdP heart dynamics model by varying the pulse shape modification factor, damping coefficients and external forcing factor while keeping the fixed value of the ventricular contraction period. The results of the proposed algorithm are compared with reference numerical solutions of Adams method to establish its correctness. Multiple independent runs are performed for the scheme, and results of statistical analyses in terms of mean absolute deviation, root-mean-square error and Nash–Sutcliffe efficiency illustrate its applicability, effectiveness and reliability.
KW - Artificial neural networks
KW - Genetic algorithms
KW - Hybrid computing
KW - Interior-point methods
KW - Model of heart
KW - Van der Pol oscillators
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U2 - 10.1007/s00521-017-2949-0
DO - 10.1007/s00521-017-2949-0
M3 - Article
AN - SCOPUS:85016112817
SN - 0941-0643
VL - 30
SP - 3651
EP - 3675
JO - Neural Computing and Applications
JF - Neural Computing and Applications
IS - 12
ER -