A Reduced Order Deep Data Assimilation model

A new Reduced Order Deep Data Assimilation (RODDA) model combining Reduced order models (ROM), Data Assimilation (DA) and Machine Learning is proposed in this paper. The RODDA model aims to improve the accuracy of Computational Fluid Dynamics (CFD) simulations. The DA model ingests information from observed data in the simulation provided by the CFD model. The results of the DA are used to train a neural network learning a function which predicts the misfit between the results of the CFD model and the DA model. Thus, the trained function is combined with the original CFD model in order to generate forecasts with implicit DA given by neural network. Due to the time complexity of the numerical models used to implement DA and the neural network, and due to the scale of the forecasting area considered for forecasting problems in real case scenarios, the implementation of RODDA mandated the introduction of opportune reduced spaces. Here, RODDA is applied to a CFD simulation for air pollution, using the CFD software Fluidity, in South London (UK). We show that, using this framework, the data forecasted by the coupled model CFD+RODDA are closer to the observations with a gain in terms of execution time with respect to the classic prediction–correction cycle given by coupling CFD with a standard DA. Additionally, RODDA predicts future observations, if not available, since these are embedded in the data assimilated state in which the network is trained on. The RODDA framework is not exclusive to air pollution, Fluidity, or the study area in South London, and therefore the workflow could be applied to different physical models if enough temporal data are available.