Accurate deep learning-based filtering for chaotic dynamics by identifying instabilities without an ensemble.

Area of Science:

• Atmospheric Science
• Dynamical Systems
• Machine Learning

Background:

• Data assimilation (DA) is crucial for analyzing chaotic systems.
• Traditional DA methods like ensemble Kalman filters and variational methods have limitations.
• Deep learning offers a novel approach to enhance DA.

Purpose of the Study:

• To investigate the use of deep learning for discovering data assimilation schemes.
• To focus on learning the analysis step in sequential DA for chaotic dynamics.
• To compare the performance of deep learning DA with existing methods.

Main Methods:

• Utilizing a residual convolutional neural network to learn the analysis step.
• Training the network on state trajectories and observations from known dynamics.
• Experimenting with the Lorenz 96 dynamics, known for spatiotemporal chaos.

Main Results:

• The learned analysis scheme achieved accuracy comparable to the best ensemble Kalman filters.
• The deep learning approach significantly outperformed variational DA alternatives.
• High accuracy was maintained even with a single state in the forecast step.

Conclusions:

• Deep learning can effectively discover accurate data assimilation schemes for chaotic systems.
• The neural network learns to identify key dynamical perturbations without ensemble covariances.
• This suggests the network learns underlying principles of the DA process as a random dynamical system.