Modeling fractional polytropic gas spheres using artificial neural network

Abstract

Lane-Emden differential equations describe different physical and astrophysical phenomena that include forms of stellar structure, isothermal gas spheres, gas spherical cloud thermal history, and thermionic currents. This paper presents a computational approach to solve the problems related to fractional Lane-Emden differential equations based on neural networks. Such a solution will help solve the fractional polytropic gas spheres problems which have different applications in physics, astrophysics, engineering, and several real-life issues. We used Artificial Neural Network (ANN) framework in its feedforward back propagation learning scheme. The efficiency and accuracy of the presented algorithm are checked by testing it on four fractional Lane-Emden equations and compared with the exact solutions for the polytopic indices n=0,1,5 and those of the series expansions for the polytropic index n=3. The results we obtained prove that using the ANN method is feasible, accurate, and may outperform other methods.

Artificial Neural Network Modeling of the Conformable Fractional Isothermal Gas Spheres

“…The results obtained reflect the applicability and efficiency of using ANN to model stellar physical characteristics (i.e., radius, mass, and density) using the fractional isothermal gas sphere. In our opinion, the present results, besides the results obtained in Nouh et al (2020), are an important step toward the composite modeling (e.g., isothermal core and polytropic envelope) of various stellar configurations using ANN.…”

“…The gradient algorithm mathematics must assure that a specific node has to be adapted in a direct rate to the error in the units it is connected to. This algorithm has been described in detail in our previous paper (Nouh et al 2020). Figure 2 shows a flow chart of an off-line back-propagation training algorithm, see Nouh et al (2020), Yadav et al (2015).…”

“…The architecture of the neural network (NN) we used in this paper for the isothermal gas sphere function the radius of the star R, while the output layer has 2 nodes, which are the mass and density at the same values of the input fractional parameters. The choice of 120 neurons in the hidden layer of the NN was decided according to the findings we reached in our previous research (Nouh et al, 2020) after testing 80,120 and 200 neurons in one hidden layer of NN (shown in Figure 1), which gave the least RMS error and the best model for the network compared to the other two configurations for both the isothermal and mass-radius relation cases.…”

“…In addition, Ahmad et al (2017) used artificial neural networks (ANNs) to compute the solution of Lane-Emden type equations. Recently, Nouh et al (2020) presented a solution to the fractional polytropic gas sphere (first kind of the Lane-Emden equation); the results indicated that the ANN method is precise when compared with other methods.…”

Prediction of the atmospheric fundamental parameters from stellar spectra using artificial neural network

“…Over the past decades, it is also well known that ANNs have acquired an eminent role in many human activity areas and have found applications in a broad range of scientific topics, including microbiology, astronomy, environment sciences, and geophysics Ozard and Morbey (1993), Almeida and Noble (2000), Tagliaferri et al (2003), Faris et al (2014), Elminir et al (2007). It was widely used in the areas of prediction, function approximation, pattern recognition, data classification, signal processing, medical diagnosis, modelling, and control, etc., El-Mallawany et al (2014), Al-Shayea (2011), Leshno et al (1993), Lippmann (1989), Zhang (2000), Nouh et al (2020). The ANN is mathematical models hinted by biological neural systems and composed of neuron models that are connected in a distributed and parallel style to imitate the knowledge acquisition and information processing of the human nervous system.…”