In this paper, we suggest a new methodology which combines Neural Networks (NN) into Data Assimilation (DA). Focusing on the structural model uncertainty, we propose a framework for integration NN with the physical models by DA algorithms, to improve both the assimilation process and the forecasting results. The NNs are iteratively trained as observational data is updated. The main DA models used here are the Kalman filter and the variational approaches. The effectiveness of the proposed algorithm is validated by examples and by a sensitivity study.

Numerical simulations are widely used as a predictive tool to better understand complex air flows and pollution transport on the scale of individual buildings, city blocks, and entire cities. To improve prediction for air flows and pollution transport, we propose a Variational Data Assimilation (VarDA) model which assimilates data from sensors into the open-source, finite-element, fluid dynamics model Fluidity. VarDA is based on the minimization of a function which estimates the discrepancy between numerical results and observations assuming that the two sources of information, forecast and observations, have errors that are adequately described by error covariance matrices. The conditioning of the numerical problem is dominated by the condition number of the background error covariance matrix which is ill-conditioned. In this paper, a preconditioned VarDA model is presented, it is based on a reduced background error covariance matrix. The Empirical Orthogonal Functions (EOFs) method is used to alleviate the computational cost and reduce the space dimension. Experimental results are provided assuming observed values provided by sensors from positions mainly located on roofs of buildings.