Solution to the ODE-mixing tank problem using artificial neural networks

This paper presents the use of artificial neural networks (ANN) to determine the solution one of the classic applications of differential equations, the mixing tank problem. An artificial neural network with feed-forward backpropagation is designed to predict the concentration of substance in the tank at any time t. The network has three layers of structure 5 - 10 - 2 and used the Levenberg-Marquadt algorithm for training. Data records used for training the network is derived from solving the ODE model of the problem numerically Testing data is composed of 100 sets, half of which is randomly sampled from the database and the other half randomly generated, given that all values fall within the constraints set. The system is evaluated by calculating the absolute error between the numerical solution and the test output of network. The response of the network is fairly accurate, having a mean error of 3.733%.