Small Ensemble-based Data Assimilation: A Machine Learning-Enhanced Data Assimilation Method with Limited Ensemble Size
arXiv:2510.15284v2 Announce Type: replace Abstract: 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