We introduce a new neural network for Data Assimilation (DA). DA is the approximation of the true state of some physical system at a given time obtained combining time-distributed observations with a dynamic model in an optimal way. The typical assimilation scheme is made up of two major steps: a prediction and a correction of the prediction by including information provided by observed data. This is the so called prediction-correction cycle. Classical methods for DA include Kalman filter (KF). KF can provide a rich information structure about the solution but it is often complex and time-consuming. In operational forecasting there is insufficient time to restart a run from the beginning with new data. Therefore, data assimilation should enable real-time utilization of data to improve predictions. This mandates the choice of an efficient data assimilation algorithm. Due to this necessity, we introduce, in this paper, the Neural Assimilation (NA), a coupled neural network made of two Recurrent Neural Networks trained on forecasting data and observed data respectively. We prove that the solution of NA is the same of KF. As NA is trained on both forecasting and observed data, after the phase of training NA is used for the prediction without the necessity of a correction given by the observations. This allows to avoid the prediction-correction cycle making the whole process very fast. Experimental results are provided and N A is tested to improve the prediction of oxygen diffusion across the Blood-Brain Barrier (BBB).
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