Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

Abstract

Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor-corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of the nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long shortterm memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data, and the trained model can be retrained effectively due to the power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using the Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging artificial intelligence friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches.

AIEADA 1.0: Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

“…Similar methods may also be found in Pawar et al (2020); Pawar and San (2021); Popov and Sandu (2021), where ML surrogates are used in lieu of the expensive forward model in ensemble techniques.…”

Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution

“…Here, instead, we can define a functional nudging map as, where the map will be inferred (e.g., LSTM model). We have tested this predictor‐corrector nudging methodology in our recent studies [254,256]. In a demonstration for solving the multiscale Lorenz 96 system [200], the chaos contaminates the solution in a short time when is solely modeled by a neural network to account for the fast fluctuating dynamics.…”

“…To decrease the computational cost required for an accurate representation of the numerous interconnected physical systems, for example, oceanic and atmospheric flows, it is pivotal to develop several classes of nested models to form the basis of highly successful applications and research at numerous weather and climate centers [226,273,286,300,343,345]. Numerous HAM tools can be used to force the large‐scale atmospheric states from global climate models onto a regional forecasting model, for example, see a canonical example in demonstrating an LSTM‐nudging approach [256].…”

Multifidelity computing for coupling full and reduced order models

“…Hence, this deviation estimate can be added as a correction term in a predictor-corrector fashion. In PCI, both inputs and outputs of the LSTM lie in the FOM space and thus the LSTM map can be considered as nudging scheme from the ROM prolongation G 1 to the FOM solution [47]. We highlight that the PCI approach can be feasible for one-dimensional (1D) problems (where the interface can be just a single point).…”