Finding the Modeling Parameters of Linear and Non-Linear Differential Equations Using ANN

Abstract

In this research article the neural network optimized with sequential quadratic programming has been exploited to numerically solve the complex systems based on linear and nonlinear ODE. The algebraic sum of log-sigmoid activation function has been manipulated in an unsupervised manner in the form of fitness function based on mean square error. The test systems involve linear system, non-linear system of homogenous and inhomogeneous nature as well as a well-known fluid system with varying magnetic parameters. The Monte Carlo simulations have been performed to see the reliability of the proposed scheme, level of convergence in optimization and computational complexity in term of time. The proposed method also outperforms as compared with the Power Series Neural Network, Euler, Modified Euler and Cosine Neural Network.