Data assimilation with hybrid modeling

Abstract

Data assimilation plays an important role in both data driven and model driven research. The celebrated Kalman filter, a typical data assimilation framework, has been widely adopted in many fields. While the classic Kalman filter relies on the theoretical model to realize filtering, several recent efforts have been made to design model-free Kalman filter which rely solely on data. In this work, we consider the gap between exact model-based method and totally model-free method, and carry out a hybrid model framework to deal with partial model and partial observation scenario. Specifically, we propose a method combining both delay embedding theory and machine learning technique to reconstruct the missing model part and such hybrid modeling is then integrated into the adaptive unscented Kalman filter framework. Overall, the hybrid modeling method is more flexible in application compared to both model-based and model-free methods. With both benchmark systems and real-world problems, we validate the effectiveness of the proposed method.