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

Bocquet, M. ORCID: https://orcid.org/0000-0003-2675-0347, Farchi, A. ORCID: https://orcid.org/0000-0002-4162-8289, Finn, T. S. ORCID: https://orcid.org/0000-0001-9585-8349, Durand, C. ORCID: https://orcid.org/0000-0001-5588-549X, Cheng, S. ORCID: https://orcid.org/0000-0002-8707-2589, Chen, Y. ORCID: https://orcid.org/0000-0002-2319-6937, Pasmans, I. ORCID: https://orcid.org/0000-0001-5076-5421 and Carrassi, A. ORCID: https://orcid.org/0000-0003-0722-5600 (2024) Accurate deep learning-based filtering for chaotic dynamics by identifying instabilities without an ensemble. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34 (9). 091104. ISSN 1089-7682 doi: 10.1063/5.0230837

Abstract/Summary

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple residual convolutional neural network, while assuming the dynamics to be known. Experiments are performed with the Lorenz 96 dynamics, which display spatiotemporal chaos and for which solid benchmarks for DA performance exist. The accuracy of the states obtained from the learned analysis approaches that of the best possibly tuned ensemble Kalman filter and is far better than that of variational DA alternatives. Critically, this can be achieved while propagating even just a single state in the forecast step. We investigate the reason for achieving ensemble filtering accuracy without an ensemble. We diagnose that the analysis scheme actually identifies key dynamical perturbations, mildly aligned with the unstable subspace, from the forecast state alone, without any ensemble-based covariances representation. This reveals that the analysis scheme has learned some multiplicative ergodic theorem associated to the DA process seen as a non-autonomous random dynamical system.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/118943
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > NCAS Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	AIP Publishing
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