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 nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long short-term 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 power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging AI-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.

Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database

“…The trade-off is that Nudging will provide for a field reconstruction that is fully respectful of all symmetries and kinematic constraints enjoyed by the PDE, something that is not always easy to achieve with Convolutional Neural Networks as discussed in the introduction. Another advantage of Nudging is that it does not need training, it works even with one damaged configuration only, it relies on the temporal evolution of the NSE to explore the phase space and provide a realistic prior for the missing information (see [74] for a recent attempt to fuse nudging with recurrent neural network). It would be interesting to compare it with other ML tools that are also based on one single image analysis to infer the statistics of the missing region [5,75].…”

A Scalable Inference Method For Large Dynamic Economic Systems

“…The state-space model stated in (6) assumes that approximation of the beta evolution function, F is known. For the complex dynamics inherent in these economic systems, it is hard to know F, and with increasing dimensions, the non-linearities would become stronger; thus linear assumption of the forward model failing [17].…”