An Artificial Neural Network approximation based decomposition approach for parameter estimation of system of ordinary differential equations

In this work a new approach for parameter estimation which is based upon decomposing the problem into two subproblems is proposed, the first subproblem generates an Artificial Neural Network (ANN) model from the given data and then the second subproblem uses the ANN model to obtain an estimate of the parameters. The analytical derivates from the ANN model obtained from the first subproblem are used for obtaining the differential terms in the formulation of the second subproblem. This greatly simplifies the parameter estimation problem. The key advantage of the proposed approach is that solution of a large optimization problem requiring high computational resources is avoided and instead two smaller problems are solved. This approach is particularly useful for large and noisy data sets and nonlinear models where ANN models are known to perform quite well and therefore plays an important role in the solution of the overall parameter estimation problem.