Latent space data assimilation by using deep learning. (27th September 2021)

• Record Type: Journal Article
• Authors: Peyron, Mathis; Fillion, Anthony; Gürol, Selime; Marchais, Victor; Gratton, Serge; Boudier, Pierre; Goret, Gael
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 147:Number 740(2021)
• Page Start: 3759
• Page End: 3777
• Publication Date: 2021-09-27
• Subjects: autoencoders -- data assimilation -- deep learning -- latent space -- Lorenz 96 -- surrogate model; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.4153
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract: Performing data assimilation (DA) at low cost is of prime concern in Earth system modeling, particularly in the era of Big Data, where huge quantities of observations are available. Capitalizing on the ability of neural network techniques to approximate the solution of partial differential equations (PDEs), we incorporate deep learning (DL) methods into a DA framework. More precisely, we exploit the latent structure provided by autoencoders (AEs) to design an ensemble transform Kalman filter with model error (ETKF‐Q) in the latent space. Model dynamics are also propagated within the latent space via a surrogate neural network. This novel ETKF‐Q‐Latent (ETKF‐Q‐L) algorithm is tested on a tailored instructional version of Lorenz 96 equations, named the augmented Lorenz 96 system, which possesses a latent structure that accurately represents the observed dynamics. Numerical experiments based on this particular system evidence that the ETKF‐Q‐L approach both reduces the computational cost and provides better accuracy than state‐of‐the‐art algorithms such as the ETKF‐Q. Abstract : Latent space data assimilation by using deep learning, Mathis Peyron, Anthony Fillion, Selime Gürol ∗, Victor Marchais, Serge Gratton, Pierre Boudier, Gael Goret. This paper exploits the latent structure provided by autoencoders to design an ensemble transform Kalman filter with model error in the latent space. The proposed methodology provides the following advantages: ( 1 ) Since any DA algorithm requires storage of vectors lying in the model space, discovering a lower‐dimensional representation induces a reduction in memory needs and computational cost; ( 2 ) Performing the DA linear analysis in the latent space obtained by AE is less susceptible to yield nonphysical solutions since the decoder is a nonlinear transformation that fits the manifold where the state trajectory statistically belongs, when such a structure exists.