Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model

Raja, Muhammad Asif Zahoor; Shah, Fiaz Hussain; Syam, Muhammed I.

doi:10.1007/s00521-017-2949-0

Cited by 64 publications

(23 citation statements)

References 55 publications

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“…Some recent applications of the evolutionary/swarming-based numerical computing are Painlevé equation-based models in random matrix theory (Raja et al 2018a), nonlinear prey-predator models (Umar 2019), Bagley-Torvik systems in fluid mechanics. (Raja 2020), nonlinear optics (Ahmad 2018a), electric activity-based model for heartbeat dynamics (Raja et al 2018b), Troesch problem in plasma physic (Majeed 2017), nonlinear doubly singular differential systems (Raja et al 2019), the dynamics of the heat conduction of human head based on nonlinear singular system (Raja et al 2018c), Thomas-Fermi atom's model (Sabir 2018), astrophysics model (Ahmad 2016), electric machines (Ahmad 2018b), circuit theory (Mehmood 2019), and mathematical models in financial studies (Ara 2018). These effective contributions motivated the authors to design the numerical computing solver for numerical treatment of DSMF-LES.…”

Section: Problem Statement and Related Workmentioning

confidence: 99%

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

et al. 2020

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In the present study, a novel fractional Meyer neuro-evolution-based intelligent computing solver (FMNEICS) is presented for numerical treatment of doubly singular multi-fractional Lane-Emden system (DSMF-LES) using combined heuristics of Meyer wavelet neural networks (MWNN) optimized with global search efficacy of genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., MWNN-GASQP. The design of novel FMNE-ICS for DSMF-LES is presented after derivation from standard Lane-Emden equation, and the singular points and shape factors along with fractional-order terms are analyzed. The MWNN modeling strength is used to represent the system model DSMF-LES in the meansquared error-based merit function and optimization of the networks is carried out with integrated optimization ability of GASQP. The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures. Moreover, the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver. Keywords Multi-fractional Lane-Emden model • Multi-singular systems • Artificial neural networks • Meyer wavelet neural networks • Sequential quadratic programming • Genetic algorithms Mathematics Subject Classification 34-XX • 34A08 • 34A34 • 82B31

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Section: Problem Statement and Related Workmentioning

confidence: 99%

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

et al. 2020

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“…The strength of artificial intelligent (AI) based computing solvers has been exploited by the research community on large scale to obtain the approximated solutions of many problems arises in broad fields of applied science and technology. Some potential, recent reported studies having paramount significance including Van-der-Pol oscillatory systems, optics, electrically conducting solids, reactive transport system, nanofluidics, nanotechnology, fluid dynamics, astrophysics, circuit theory, plasma, atomic physics, bioinformatics, energy, power and functional mathematics see [24][25][26][27][28][29][30][31][32][33][34] and references cited therein. The said information is the motivational affinities to investigate in AI base numerical computing solver for the COVID-19 model.…”

Section: Problem Statement With Significancementioning

confidence: 99%

Intelligent computing with Levenberg–Marquardt artificial neural networks for nonlinear system of COVID-19 epidemic model for future generation disease control

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The aim of this work is to design an intelligent computing paradigm through Levenberg-Marquardt artificial neural networks (LMANNs) for solving the mathematical model of Corona virus disease 19 (COVID-19) propagation via human to human interaction. The model is represented with systems of nonlinear ordinary differential equations represented with susceptible, exposed, symptomatic and infectious, super spreaders, infection but asymptomatic, hospitalized, recovery and fatality classes, and reference dataset of the COVID-19 model is generated by exploiting the strength of explicit Runge-Kutta numerical method for metropolitans of China and Pakistan including Wuhan, Karachi, Lahore, Rawalpindi and Faisalabad. The created dataset is arbitrary used for training, validation and testing processes for each cyclic update in Levenberg-Marquardt backpropagation for numerical treatment of the dynamics of COVID-19 model. The effectiveness and reliable performance of the design LMANNs are endorsed on the basis of assessments of achieved accuracy in terms of mean squared error based merit functions, error histograms and regression studies.

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“…, which is asymmetric with respect to the variable x, for further updates in (4) it is modified as [4], [29], [56], [58]:…”

Section: Heart Beat Modeling Based On Van Der Pol Nonlinear Oscillatormentioning

confidence: 99%

Analysis of Oscillatory Behavior of Heart by Using a Novel Neuroevolutionary Approach

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This paper aims at the analysis of the VdP heartbeat mathematical model. We have analysed the conditionality of a mathematical model which represents the oscillatory behaviour of the heart. A novel neuroevolutionary approach is chosen to analyse the mathematical model. The characteristics of the cardiac pulse of the heart are examined by considering two major scenarios with sixteen different cases. Artificial neural networks (ANNs) are constructed to obtain the best solutions for the heartbeat model. Unknown weights are finely tuned by a combination of a global search technique the Harris Hawks Optimizer (HHO) and a local search technique the Interior Point Algorithm (IPA). Stable behaviour of solutions obtained by considering different cases demonstrates that the model under consideration is well-conditioned. The accuracy of our novel procedure is established by getting the lowest residual errors in our solution for all cases. Graphical and statistical analysis are added to further elaborate the accuracy of our approach. INDEX TERMSCardiac pulse model, hybridized soft computing, artificial neural networks, non-linear ordinary differential equations, heuristics, interior-point algorithm, Harris Hawks optimizer. Ph.D. degree in software engineering from De Montfort University, in 2015. From 2004 to 2007, he worked in the Software Development Industry, where he implemented several systems and solutions for a National Academic Institution. His research interests include algorithms, semantic web, and optimization techniques. He focuses on enhancing real-world matching systems using machine learning and data analytics in the context of supporting decision-making.

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Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model

Cited by 64 publications

References 55 publications

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

Intelligent computing with Levenberg–Marquardt artificial neural networks for nonlinear system of COVID-19 epidemic model for future generation disease control

Analysis of Oscillatory Behavior of Heart by Using a Novel Neuroevolutionary Approach

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