Artificial Neural Network Approach to Study Imprecisely Defined Nonlinear Systems With Case Studies

This paper introduces an alternative method for analysing mathematical models by combining an artificial neural network (ANN) with a modified Levenberg-Marquardt (LM) optimization approach to solve fuzzy systems of nonlinear equations. The proposed method transforms fuzzy equations into an unconstrained optimization problem by employing triangular fuzzy numbers (TFNs) and utilizing a membership value to map fuzzy constraints into crisp values. A feed-forward neural network (FFNN) is used to generate outputs based on initial guesses for the field variables, and the ANN-LM algorithm optimizes the solution by minimizing the error between predicted and target values. The effectiveness of the approach is validated through convergence analysis and case studies, including applications in electrical circuits and static structural problem. The developed algorithm is coded with the MATLAB software, and the results are examined through numerical examination and graphical visualization. The results demonstrate that the proposed approach outperforms various traditional exact and numerical methods, providing a reliable and guaranteed solution to the field variables.