F.P. Harter H.F. de Campos Velho (2007): New Approach to Applying Neural Network in Nonlinear Dynamic Model, Applied Mathematgical Modelling (submitted).

Abstract: In this work, Radial Basis Function Neural Network (RBF-NN) is applied in order to emulate an Extended Kalman Filter (EKF) in a data assimilation scenario. The dynamical model studied here is the 1-Dimensional Shallow Water Equations (DYNAMO-1D), simple when compared with the operational primitive equations models (OPEM), but rich in atmospheric motions such as Rossby and gravity waves. It has been shown in the literature that the ability of the EKF to track non-linear models depends on the frequency and accuracy of the observations and model errors. In some cases, just fourth-order moments EKF work well, but will be unwieldy when applied to high–dimensional state space, such as OPEM. Artificial Neural Network (ANN) could be an alternative solution for this computational complexity problem, once the ANN could be trained offline with a high order Kalman filter, even thought this Kalman filter has high computational cost (which is not a problem during ANN training phase). The results reached in this work encourage us to apply this technique on OPEM. However, it is not yet possible to assure convergence in high dimensional problems.