Modified Levenberg-Marquardt Neural Network Method to Investigate Optimum Height of a Water Tank Problem

This paper presents a modified Levenberg-Marquardt neural network approach to investigate governing mathematical equations. The mentioned physical problem is modelled mathematically and then the hybrid neural network is utilized to obtain the field variables. Idea of the proposed method is divided into three steps, first, the mathematical model is transformed into an algebraic equation and for the same incremental search method is applied to find the initial field variables. Secondly, using the initial values, feed forward neural network is constructed to get the output. Finally, the output is analysed with the Levenberg-Marquardt approach to get the optimal solution. A case study viz. water tank problem is analysed here. Using the volume equation of the tank, the maximum optimal height of the tank is obtained. From this investigation it is noticed that the proposed approach performs better than various standard exact and numerical methods as well as the incremental search technique and Levenberg-Marquardt method ensures a guaranteed solution.