A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system

Abstract

The current study is related to present a novel neuro-swarming intelligent heuristic for nonlinear second-order Lane–Emden multi-pantograph delay differential (NSO-LE-MPDD) model by applying the approximation proficiency of artificial neural networks (ANNs) and local/global search capabilities of particle swarm optimization (PSO) together with efficient/quick interior-point (IP) approach, i.e., ANN-PSOIP scheme. In the designed ANN-PSOIP scheme, a merit function is proposed by using the mean square error sense along with continuous mapping of ANNs for the NSO-LE-MPDD model. The training of these nets is capable of using the integrated competence of PSO and IP scheme. The inspiration of the ANN-PSOIP approach instigates to present a reliable, steadfast, and consistent arrangement relates the ANNs strength for the soft computing optimization to handle with such inspiring classifications. Furthermore, the statistical soundings using the different operators certify the convergence, accurateness, and precision of the ANN-PSOIP scheme.

Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems

“…The stochastic soft computing platform has been extensively used by the research community for addressing different applications of paramount interest arising in a broad domain of applied science and engineering. A few examples exploiting the strength of AI methods as reliable and effective solution approaches include online learning, scheduling via multi-objective optimization [41], nonlinear Falkner-Skan systems [42], the berth scheduling problem at marine container terminals [43], the entropy generation model [44], density estimation [45], the vehicle routing problem [46], nonlinear Lane-Emden multipantograph delay differential systems [47], the identification of differences between bacterial and viral meningitis [48], the Bouc-Wen hysteresis model for piezostage actuators [49], data classification [50], and the parameter estimation of power signals [51]. All these illustrations prove the worth of heuristics and meta-heuristics methodologies.…”

Application of a Novel Collocation Approach for Simulating a Class of Nonlinear Third-Order Lane–Emden Model

“…ese extensive works on the solutions of PD models open the door to exploit the wider applications of similar models of the reallife phenomenon. For more details regarding the applications and techniques for solving the PD models, one may refer to [20][21][22][23] and the references therein.…”

Swarm Intelligence Procedures Using Meyer Wavelets as a Neural Network for the Novel Fractional Order Pantograph Singular System

“…The numerical discussions of the FOPSS are provided based on the fractional Meyer wavelets (FMWs) as a neural network (NN) with the optimization procedures of global/local search procedures of particle swarm optimization (PSO) and interior-point algorithm (IPA), i.e., FMWs-NN-PSOIPA. The stochastic schemes based on numerical measures is applied to solve a variety of applications [33][34][35][36][37][38][39][40], and a few potential recently reported applications include the solution of nonlinear Lane-Emden multi-pantograph delay based ordinary differential equations (ODEs) [41], Gudermannian neural networks for sODEs [42], neuroswarming approach to singular with multiple delay ODEss [43], intelligent backpropagated networks for solving Lene-Emden singular ordinary differential systems with pantograph delays [44], novel design of Morlet wavelet neural networks for solving singular pantograph nonlinear differential models [45], third kind of multi-singular nonlinear systems [46], novel design of evolutionary integrated heuristics for singular systems [47], Morlet wavelet neural networks for solving higher order singular nonlinear ODEs [48] and wavelet analysis on some surfaces of revolution [49]. All these applications inspire the authors to investigate the design of FOPSS, which has never been implemented nor treated, by using the proposed heuristics of FMWs-NN-PSOIPA.…”