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Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models

Bocquet, M., Brajard, J., Carrassi, A. and Bertino, L. (2019) Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models. Nonlinear Processes in Geophysics, 26 (3). pp. 143-162. ISSN 1607-7946

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To link to this item DOI: 10.5194/npg-26-143-2019

Abstract/Summary

Recent progress in machine learning has shown how to forecast and, to some extent, learn the dynamics of a model from its output, resorting in particular to neural networks and deep learning techniques. We will show how the same goal can be directly achieved using data assimilation techniques without leveraging on machine learning software libraries, with a view to high-dimensional models. The dynamics of a model are learned from its observation and an ordinary differential equation (ODE) representation of this model is inferred using a recursive nonlinear regression. Because the method is embedded in a Bayesian data assimilation framework, it can learn from partial and noisy observations of a state trajectory of the physical model. Moreover, a space-wise local representation of the ODE system is introduced and is key to coping with high-dimensional models. It has recently been suggested that neural network architectures could be interpreted as dynamical systems. Reciprocally, we show that our ODE representations are reminiscent of deep learning architectures. Furthermore, numerical analysis considerations of stability shed light on the assets and limitations of the method. The method is illustrated on several chaotic discrete and continuous models of various dimensions, with or without noisy observations, with the goal of identifying or improving the model dynamics, building a surrogate or reduced model, or producing forecasts solely from observations of the physical model.

Item Type:Article
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Faculty of Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO)
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:90672
Publisher:Copernicus

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