Adaptive Neural Network filter and its application to data assimilation in 2D water pollution model

This study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers, in comparison to the widely used variational method. The Adaptive Neural Network (ANN) filter, proposed in this paper, is sequential and stable even for unstable dynamical systems, with the gain parameters as control variables. This ANN filter is called ANNSEIKF0, being based on the Adaptive Singular Evolutive Interpolated Kalman Filter (ASEIKF0). To deal with the uncertainty of the system parameters and of the noise covariance, the proposed filter ANNSEIKF0 makes use of the covariance of reduced rank iterated during assimilation process and of some pertinent gain parameters tuned adaptively to yield the minimum prediction error for the system output. The computational burden in the implementation of this filter is reduced drastically due to applying the optimization tool known as a simultaneous perturbation stochastic approximation algorithm, which requires only two integrations of the numerical model. No iterative loop is required at each assimilation instant as usually happens with the standard gradient descent optimization algorithms. Data assimilation experiment, carried out by the NNSEIKF0 (Neural network based on SEIKF0) and the ANNSEIKF0, is implemented for the Thanh Nhan Lake in Hanoi and the performance comparison between these two filters is given to show the high efficiency of the proposed ANNSEIKF0.