A Neuro-Evolution Heuristic Using Active-Set Techniques to Solve a Novel Nonlinear Singular Prediction Differential Model

Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Botmart, Thongchai; Weera, Wajaree

doi:10.3390/fractalfract6010029

Cited by 19 publications

(8 citation statements)

References 28 publications

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“…In this section, the existing section shows the stochastic operator performances for solving the fractional order computational myeloma bone disease model with LVMBPNN. In the literature, stochastic software solvers have been investigated to solve complicated, singular, and rigid systems [42,43]. Recently, the simulation based on the food chain function [44], infection control model [45], Lane-Emden systems [46], functional order approaches [47], and nonlinear dynamic HIV systems [48][49][50].…”

Section: Fractional Order Mathematical Bone Remodeling Systemmentioning

confidence: 99%

Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

Yotha¹,

Hiader²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

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This study aims to solve the nonlinear fractional-order mathematical model (FOMM) by using the normal and dysregulated bone remodeling of the myeloma bone disease (MBD). For the more precise performance of the model, fractional-order derivatives have been used to solve the disease model numerically. The FOMM is preliminarily designed to focus on the critical interactions between bone resorption or osteoclasts (OC) and bone formation or osteoblasts (OB). The connections of OC and OB are represented by a nonlinear differential system based on the cellular components, which depict stable fluctuation in the usual bone case and unstable fluctuation through the MBD. Untreated myeloma causes by increasing the OC and reducing the osteoblasts, resulting in net bone waste the tumor growth. The solutions of the FOMM will be provided by using the stochastic framework based on the Levenberg-Marquardt backpropagation (LVMBP) neural networks (NN), i.e., LVMBPNN. The mathematical performances of three variations of the fractional-order derivative based on the nonlinear disease model using the LVMPNN. The static structural performances are 82% for investigation and 9% for both learning and certification. The performances of the LVMBPNN are authenticated by using the results of the Adams-Bashforth-Moulton mechanism. To accomplish the capability, steadiness, accuracy, and ability of the LVMBPNN, the performances of the error histograms (EHs), mean square error (MSE), recurrence, and state transitions (STs) will be provided.

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Section: Fractional Order Mathematical Bone Remodeling Systemmentioning

confidence: 99%

Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

Yotha¹,

Hiader²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

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“…Recently, many systems that have been designed with the terminology of the Lane-Emden model. Few of them are the singular 2nd and 3rd pantograph model, 4th, 5th order and 6th kinds of functional singular systems, prediction, delay and pantograph form of the singular models [36][37][38][39][40][41][42][43][44] . Based on these applications, the authors are inspired to construct a novel SO-PSDDM.…”

Section: A Novel Design Of So-psddmmentioning

confidence: 99%

A neuro swarm procedure to solve the novel second order perturbed delay Lane-Emden model arising in astrophysics

Sabir

Saïd

Al‐Mdallal

et al. 2022

Sci Rep

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The current work provides a mathematical second order perturbed singular delay differential model (SO-PSDDM) by using the standard form of the Lane-Emden model. The inclusive structures based on the delay terms, singular-point and perturbation factor and shape forms of the SO-PSDDM are provided. The novel form of the SO-PSDDM is numerically solved by using the procedures of artificial neural networks (ANNs) along with the optimization measures based on the swarming procedures (PSO) and interior-point algorithm (IPA). An error function is optimized through the swarming PSO procedure along with the IPA to solve the SO-PSDDM. The precision, substantiation and validation are observed for three problems of the SO-PSDDM. The exactness of the novel SO-PSDDM is observed by comparing the obtained and exact solutions. The reliability, stability and convergence of the proposed stochastic algorithms are observed for 30 independent trials to solve the novel SO-PSDDM.

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“…Executing the process of PSO is easy and straightforward due to the short requirements of the memory [31]. Few recent submissions of PSO are the parameter estimation [32], wind turbine through pitch control model [33], benchmark optimization [34], reactive power dispatch models [35], electric circuits based nonlinear systems [36], the adaptive tune of PID controller [37] and approximation of undrained based shear soil strength [38].…”

Section: Optimization: Pso-ipamentioning

confidence: 99%

Swarming Computational Techniques for the Influenza Disease System

Noinang¹,

Sabir²,

Altamirano³

et al. 2022

Computers, Materials &Amp; Continua

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The current study relates to designing a swarming computational paradigm to solve the influenza disease system (IDS). The nonlinear system's mathematical form depends upon four classes: susceptible individuals, infected people, recovered individuals and cross-immune people. The solutions of the IDS are provided by using the artificial neural networks (ANNs) together with the swarming computational paradigm-based particle swarm optimization (PSO) and interior-point scheme (IPA) that are the global and local search approaches. The ANNs-PSO-IPA has never been applied to solve the IDS. Instead a merit function in the sense of mean square error is constructed using the differential form of each class of the IDS and then optimized by the PSOIPA. The correctness and accuracy of the scheme are observed to perform the comparative analysis of the obtained IDS results with the Adams solutions (reference solutions). An absolute error in suitable measures shows the precision of the proposed ANNs procedures and the optimization efficiency of the PSOIPA. Furthermore, the reliability and competence of the proposed computing method are enhanced through the statistical performances.

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A Neuro-Evolution Heuristic Using Active-Set Techniques to Solve a Novel Nonlinear Singular Prediction Differential Model

Cited by 19 publications

References 28 publications

Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

A neuro swarm procedure to solve the novel second order perturbed delay Lane-Emden model arising in astrophysics

Swarming Computational Techniques for the Influenza Disease System

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