We present and assess a method to reduce the computational cost of performing ensemble-based data assimilation (DA) for reacting flows in multiple-query scenarios, i.e. scenarios where multiple simulations are performed on systems with similar underlying dynamics. The accuracy of the DA, which depends on the accuracy of the sample covariance, improves with the ensemble size, but results in a commensurate increase to computational cost. To reduce the ensemble size while maintaining accurate covariance, we propose a data-driven approach to augment the covariance based on the statistical behaviour learned from previous model evaluations. We assess our augmentation method using one-dimensional model problems and a two-dimensional synthetic reacting flow problem. We show in all these cases that ensemble size, and thus computational cost, may be reduced by a factor of three to four while maintaining accuracy.

我们提出并评估了一种方法来降低执行基于集合的数据同化 (DA) 以在多查询场景中反应流的计算成本，即在具有相似基础动态的系统上执行多个模拟的场景。DA 的准确性取决于样本协方差的准确性，随着集成规模的增加而提高，但会导致计算成本相应增加。为了在保持准确协方差的同时减小集合大小，我们提出了一种数据驱动的方法，基于从先前模型评估中学到的统计行为来增加协方差。我们使用一维模型问题和二维合成反应流问题来评估我们的增强方法。我们在所有这些情况下展示了集合大小，因此计算成本，