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.

本文提出了一种新的降阶深度数据同化（RODDA）模型，该模型结合了降序模型（ROM），数据同化（DA）和机器学习。RODDA模型旨在提高计算流体动力学（CFD）模拟的准确性。在CFD模型提供的模拟中，DA模型从观察到的数据中提取信息。DA的结果用于训练学习预测CFD模型和DA模型的结果不匹配的函数的神经网络。因此，将训练后的函数与原始CFD模型相结合，以通过神经网络给出具有隐式DA的预测。由于用于实现DA和神经网络的数值模型的时间复杂性，并且由于考虑了在实际情况下进行预测的预测区域的规模，RODDA的实施要求引入适当的缩减空间。在这里，使用CFD软件Fluidity（位于英国南伦敦）将RODDA应用于CFD模拟中的空气污染。我们表明，使用这种框架，CFD + RODDA耦合模型所预测的数据更接近于观测值，并且相对于将CFD与标准DA耦合所给出的经典预测-校正周期而言，执行时间有所增加。此外，RODDA会预测将来的观测结果（如果不可用），因为这些观测值嵌入在训练网络的数据同化状态中。RODDA框架不仅限于空气污染，流动性或伦敦南部的研究区域，因此，如果有足够的时间数据可用，则可以将工作流应用于不同的物理模型。