Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models
Source abstract
Abstract
In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Iterative Methods for Nonlinear Equations · Matrix Theory and Algorithms
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu, Sabah 88400, Malaysia
Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Pakistan
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan
Post-Graduation Program in Electrical Engineering, Federal University of Piauí (UFPI), Teresina-PI 64049-550, Brazil
Covilhã Delegation, Instituto de Telecomunicações, 6201-001 Covilhã, Portugal
Faculty of Computer Science and Information Technology, Universiti Malaysia Sarawak, Kota Samarahan 94300, Malaysia
Department of Electronics and Communication Engineering, JECRC University Jaipur, Rajasthan 303905, India
Department of Mathematics and Statistics, Mutah University Jordan, Mu’tah 61710, Jordan
Data Science and Cybersecurity Center, Dept of Electrical Engineering and Computer Science, Howard University, Washington, DC 20059, USA
Funding
Universiti Malaysia Sabah
References (63)
Show source-provided references
1. On the Theoretical Temperature of the Sun, under the Hypothesis of a gaseous Mass maintaining its Volume by its internal Heat and depending on the laws of gases as known to terrestrial Experiment10.2475/ajs.s2-50.148.57 ↗
2. Emden, R. (1907). Gaskugeln Teubner, Scientific Research.
3. Neural network methods to solve the Lane–Emden type equations arising in thermodynamic studies of the spherical gas cloud model10.1007/s00521-016-2400-y ↗
4. Novel design of Morlet wavelet neural network for solving second order Lane–Emden equation10.1016/j.matcom.2020.01.005 ↗
5. Nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem with degenerate density dependent viscosities10.1007/s00220-016-2753-1 ↗
6. New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator10.1140/epjp/i2019-12561-x ↗
7. Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory10.1080/09540091.2015.1092499 ↗
8. Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method10.1007/s10910-013-0260-6 ↗
9. On a class of singular Gierer–Meinhardt systems arising in morphogenesis10.1016/j.crma.2006.12.008 ↗
10. Bhrawy, A.H., Alofi, A.S., and Van Gorder, R.A. (2014). An efficient collocation method for a class of boundary value problems arising in mathematical physics and geometry. Abstract and Applied Analysis, Hindawi Publishing Corporation.10.1155/2014/425648 ↗
11. Solution of an Integro-Differential Equation Arising in Oscillating Magnetic Fields Using He’s Homotopy Perturbation Method10.2528/PIER07090403 ↗
12. Combined effects in nonlinear problems arising in the study of anisotropic continuous media10.1016/j.na.2011.01.037 ↗
13. On coupled Lane-Emden equations arising in dusty fluid models10.1088/1742-6596/268/1/012006 ↗
14. Solving a new design of nonlinear second-order Lane–Emden pantograph delay differential model via Bernoulli collocation method10.1140/epjp/s13360-020-00449-x ↗
15. A new analytic algorithm of Lane–Emden type equations
16. Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs10.1016/S0010-4655(01)00415-5 ↗
17. Integrated intelligent computing paradigm for nonlinear multi-singular third-order Emden–Fowler equation10.1007/s00521-020-05187-w ↗
18. Zhang, H., and Qing, H. (2017, January 20–23). Cooperative bat searching algorithm: A combined perspective from multiagent coordination and swarm intelligence. Proceedings of the 2017 13th IEEE Conference on Automation Science and Engineering (CASE), Xi’an, China.10.1109/COASE.2017.8256292 ↗
19. Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation10.1016/j.matcom.2020.06.021 ↗
20. Numerical solution of doubly singular nonlinear systems using neural networks-based integrated intelligent computing10.1007/s00521-017-3110-9 ↗
21. Novel applications of intelligent computing paradigms for the analysis of nonlinear reactive transport model of the fluid in soft tissues and microvessels10.1007/s00521-019-04203-y ↗
22. A new heuristic computational solver for nonlinear singular Thomas–Fermi system using evolutionary optimized cubic splines10.1140/epjp/s13360-019-00066-3 ↗
23. Design of neuro-swarming-based heuristics to solve the third-order nonlinear multi-singular Emden–Fowler equation10.1140/epjp/s13360-020-00424-6 ↗
24. Intelligent computing strategy to analyze the dynamics of convective heat transfer in MHD slip flow over stretching surface involving carbon nanotubes10.1016/j.jtice.2017.08.016 ↗
25. Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system10.1016/j.aej.2020.04.051 ↗
26. A stochastic computational intelligent solver for numerical treatment of mosquito dispersal model in a heterogeneous environment10.1140/epjp/s13360-020-00557-8 ↗
27. Continuous Genetic Algorithm as a Novel Solver for Stokes and Nonlinear Navier Stokes Problems
28. Neuro-swarm intelligent computing to solve the second-order singular functional differential model10.1140/epjp/s13360-020-00440-6 ↗
29. Stochastic numerical technique for solving HIV infection model of CD4+ T cells10.1140/epjp/s13360-020-00417-5 ↗
30. Design of artificial neural network models optimized with sequential quadratic programming to study the dynamics of nonlinear Troesch’s problem arising in plasma physics10.1007/s00521-016-2530-2 ↗
31. Neuro-heuristics for nonlinear singular Thomas-Fermi systems10.1016/j.asoc.2018.01.009 ↗
32. Intelligent computing for numerical treatment of nonlinear prey–predator models10.1016/j.asoc.2019.04.022 ↗
33. Stochastic numerical solver for nanofluidic problems containing multi-walled carbon nanotubes10.1016/j.asoc.2015.10.015 ↗
34. Application of GA-BP neural network algorithm in killing well control system10.1007/s00521-020-05298-4 ↗
35. Unsupervised constrained neural network modeling of boundary value corneal model for eye surgery10.1016/j.asoc.2019.105826 ↗
36. Design of neuro-computing paradigms for nonlinear nanofluidic systems of MHD Jeffery–Hamel flow10.1016/j.jtice.2018.05.046 ↗
37. Improved estimation of Cetane number of fatty acid methyl esters (FAMEs) based biodiesels using TLBO-NN and PSO-NN models10.1016/j.fuel.2018.05.166 ↗
38. Relative Building-Block Fitness and the Building Block Hypothesis
39. Quantum genetic algorithm for dynamic economic dispatch with valve-point effects and including wind power system10.1016/j.ijepes.2010.08.014 ↗
40. Enhanced prediction of heart disease with feature subset selection using genetic algorithm
41. A new stochastic computing paradigm for the dynamics of nonlinear singular heat conduction model of the human head10.1140/epjp/i2018-12153-4 ↗
42. Genetic-Algorithm-Based Optimization Approach for Energy Management10.1109/TPWRD.2012.2219598 ↗
43. In silico discovery of metal-organic frameworks for precombustion CO2 capture using a genetic algorithm10.1126/sciadv.1600909 ↗
44. Gai, K., Qiu, M., and Zhao, H. (2017). Cost-aware multimedia data allocation for heterogeneous memory using genetic algorithm in cloud computing. IEEE Trans. Cloud Comput.
45. Design of bio-inspired heuristic technique integrated with interior-point algorithm to analyze the dynamics of heartbeat model10.1016/j.asoc.2016.10.009 ↗
46. Ball, M.G., Qela, B., and Wesolkowski, S. (2015). A Review of the Use of Computational Intelligence in the Design of Military Surveillance Networks. Complex Networks & Their Applications IX., Springer International Publishing.10.1007/978-3-319-26450-9_24 ↗
47. Modeling and optimization of anaerobic codigestion of potato waste and aquatic weed by response surface methodology and artificial neural network coupled genetic algorithm10.1016/j.biortech.2016.04.068 ↗
48. A Hybrid with Cross-Entropy Method and Sequential Quadratic Programming to Solve Economic Load Dispatch Problem10.1109/JSYST.2013.2297471 ↗
49. A novel chaotic differential evolution hybridized with quadratic programming for short-term hydrothermal coordination10.1007/s00521-017-2940-9 ↗
50. A superlinear convergence feasible sequential quadratic programming algorithm for bipedal dynamic walking robot via discrete mechanics and optimal control10.1002/oca.2228 ↗
51. Optimization of a multiproduct economic production quantity problem with stochastic constraints using sequential quadratic programming10.1016/j.knosys.2015.04.001 ↗
52. Formulating the optimization problem when using sequential quadratic programming applied to a simple LNG process10.1016/j.compchemeng.2015.06.003 ↗
53. Optimal design of heating system in rapid thermal cycling blow mold by a two-step method based on sequential quadratic programming10.1016/j.icheatmasstransfer.2018.06.006 ↗
54. Engelbrecht, J.J., and Engelbrecht, J.A. (December, January 30). Optimal attitude and flight vector recovery for large transport aircraft using sequential quadratic programming. Proceedings of the 2016 Pattern Recognition Association of South Africa and Robotics and Mechatronics International Conference (PRASA-RobMech), Stellenbosch, South Africa.10.1109/RoboMech.2016.7813153 ↗
55. Schröder, K., Gebhardt, C., and Rolfes, R. (2016, January 5–8). Damage Localization at Wind Turbine Support Structures Using Sequential Quadratic Programming for Model Updating. Proceedings of the 8th European Workshop on Structural Health Monitoring, Bilbao, Spain.
56. Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm10.1007/s10898-009-9482-3 ↗
57. Design of a Nonlinear SITR Fractal Model Based on the Dynamics of a Novel Coronavirus (COVID)10.1142/S0218348X20400265 ↗
58. Sánchez, G., Sabir, Z., Günerhan, H., and Baskonus, H.M. (2020). Analytical and Approximate Solutions of a Novel Nervous Stomach Mathematical Model. Discret. Dyn. Nat. Soc., 2020.10.1155/2020/5063271 ↗
59. Sabir, Z., Imran, A., Umar, M., Zeb, M., Shoaib, M., and Raja, M.A.Z. (2020). A numerical approach for two-dimensional Sutterby fluid flow bounded at a stagnation point with an inclined magnetic field and thermal radiation impacts. Therm. Sci., 186.
60. Three-dimensional flow of Casson nanofluid over a stretched sheet with chemical reactions, velocity slip, thermal radiation and Brownian motion10.2298/TSCI190625339U ↗
61. A Computational Analysis of Two-Phase Casson Nanofluid Passing a Stretching Sheet Using Chemical Reactions and Gyrotactic Microorganisms10.1155/2019/1490571 ↗
62. Numerical treatment for the three-dimensional eyring-powell fluid flow over a stretching sheet with velocity slip and activation energy10.1155/2019/9860471 ↗
63. The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion10.1155/2020/2010568 ↗