A novel design of a sixth-order nonlinear modeling for solving engineering phenomena based on neuro intelligence algorithm

The current study aims to present a novel design of a sixth-order (SO) nonlinear Emden-Fowler nonlinear system (SO-NSEFM) along with its five types. The novel design of SO-NSEFM is achieved using the typical second-order Emden-Fowler system. The detail of the singularity and shape factors is presented for each type of the SO-NSEFM. Three different examples of each type of the designed SO-NSEFM will be solved using the supervised neural network (SNN) Levenberg-Marquardt backpropagation approach (LMBA), i.e., SNN-LMBA. A reference dataset using the spectral collocation scheme with the proposed SNN-LMBA will be established for the designed SO-NSEFM. The achieved approximate outcomes of the designed SO-NSEFM are accessible using the procedures of testing, verification, and training of the proposed neural networks to reduce the MSE. For the efficiency, correctness, and effectiveness of the proposed SNN-LMBA, the investigations are presented through the proportional performances of regression, MSE results, correlation and error histograms (EHs), and regression.

Automated summary

The current study aims to present a novel design of a sixth-order nonlinear Emden-Fowler system and provides detailed characteristics for each type of the system. Examples of the designed system are solved using a supervised neural network approach, and a reference dataset is established. The results of the study show that the proposed method is efficient, correct, and effective in reducing mean square error and improving correlation.