Bio-inspired computational heuristics to study Lane–Emden systems arising in astrophysics model

Abstract

This study reports novel hybrid computational methods for the solutions of nonlinear singular Lane–Emden type differential equation arising in astrophysics models by exploiting the strength of unsupervised neural network models and stochastic optimization techniques. In the scheme the neural network, sub-part of large field called soft computing, is exploited for modelling of the equation in an unsupervised manner. The proposed approximated solutions of higher order ordinary differential equation are calculated with the weights of neural networks trained with genetic algorithm, and pattern search hybrid with sequential quadratic programming for rapid local convergence. The results of proposed solvers for solving the nonlinear singular systems are in good agreements with the standard solutions. Accuracy and convergence the design schemes are demonstrated by the results of statistical performance measures based on the sufficient large number of independent runs.

Design of Morlet Wavelet Neural Network for Solving a Class of Singular Pantograph Nonlinear Differential Models

“…Fig. 1 presents the 3, 6 and 10 neurons based on the equations (19)(20)(21)(22)(23)(24)(25)(26)(27) to get the best weights of the approximate results of the MWNN-GAIPAS. Fig.…”

“…It is not easy and always a big challenge for the research community to solve the Lane-Emden form of the model due to singular-point at the origin. The general form of the singular Lane-Emden equation is given as [23][24][25]: where I is a constant, Ω ≥ 1 represents a shape factor, the singularity arises at τ = 0. The present study is related to solve a singular pantograph (proportional delay with parameter a) differential model and is given as [26]: The above equation shows a singular form of the pantograph differential model, the multiple delays are noticed in the 1 st and 2 nd terms.…”

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

“…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.…”

Machine Learning for Modeling the Singular Multi-Pantograph Equations

“…The application of multi-pantograph differential equations (MDEs) is expanding into various branches of science such as modeling of cell-growth [ 1 ], electrodynamics [ 2 ], number theory [ 3 ], electrodynamics, astrophysics [ 4 ], atomic physics [ 5 ], among many others.…”