Nudging‐Based Data Assimilation Method for Error Correction Coupled With Huber Loss Functions and BiLSTM‐GRU Hybrids

Abstract In machine learning (ML) algorithms, neural networks (NNs) can effectively learn the mapping between initial condition errors and system states through training. To reduce model errors in data assimilation, this work proposes an optimization strategy for the data assimilation (DA) process based on ML methods. A novel hybrid deep learning approach is introduced, which combines bidirectional long short‐term memory (BiLSTM) networks and gated recurrent units (GRUs) in a serial processing manner. First, the BiLSTM‐GRU hybrid method is trained by modeling the residuals between the system's observational data and the ensemble Kalman filter (EnKF) assimilation results, which are used as inputs to learn the error correction process. Second, the Huber loss function is used to quantify the error, and the network model's parameters are updated on the basis of the loss feedback to correct model errors in the data assimilation system. Additionally, the hybrid model incorporates nudging by introducing a certain amount of “relaxation” in each iteration, gradually approaching the actual solution. Ultimately, comprehensive experiments demonstrate that the BiLSTM‐GRU hybrid, even after strengthening traditional EnKF with inflation, localization, and stabilization, consistently achieves superior robustness across varying dynamical regimes, ensemble sizes, observation densities, and noise levels, highlighting its scalability for nonlinear chaotic systems.