Ensemble-based data assimilation (DA) methods have become increasingly popular due to their inherent ability to address nonlinear dynamic problems. However, these methods often face a trade-off between analysis accuracy and computational efficiency, as larger ensemble sizes required for higher accuracy also lead to greater computational cost. In this study, we propose a novel machine learning-based data assimilation approach that combines the traditional ensemble Kalman filter (EnKF) with a fully connected neural network (FCNN). Specifically, our method uses a relatively small ensemble size to generate preliminary yet suboptimal analysis states via EnKF. A FCNN is then employed to learn and predict correction terms for these states, thereby mitigating the performance degradation induced by the limited ensemble size. We evaluate the performance of our proposed EnKF-FCNN method through numerical experiments involving Lorenz systems and nonlinear ocean wave field simulations. The results consistently demonstrate that the new method achieves higher accuracy than traditional EnKF with the same ensemble size, while incurring negligible additional computational cost. Moreover, the EnKF-FCNN method is adaptable to diverse applications through coupling with different models and the use of alternative ensemble-based DA methods.

翻译：集合数据同化方法因其固有的处理非线性动态问题的能力而日益受到欢迎。然而，这些方法常常面临分析精度与计算效率之间的权衡，因为提高精度所需的大规模集合也会导致更高的计算成本。在本研究中，我们提出了一种新颖的基于机器学习的数据同化方法，该方法将传统的集合卡尔曼滤波与全连接神经网络相结合。具体而言，我们的方法使用相对较小的集合规模，通过EnKF生成初步但次优的分析状态。随后，利用FCNN学习并预测这些状态的校正项，从而减轻由有限集合规模引起的性能下降。我们通过涉及洛伦兹系统和非线性海洋波场模拟的数值实验，评估了所提出的EnKF-FCNN方法的性能。结果一致表明，新方法在相同集合规模下比传统EnKF实现了更高的精度，同时产生的额外计算成本可忽略不计。此外，EnKF-FCNN方法可通过与不同模型耦合以及使用替代的集合数据同化方法，适应多样化的应用场景。