Data Assimilation Networks. (13th April 2023)

• Record Type: Journal Article
• Authors: Boudier, Pierre; Fillion, Anthony; Gratton, Serge; Gürol, Selime; Zhang, Sixin
• Is Part Of: Journal of advances in modeling earth systems. Volume 15:Number 4(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-04-13
• Subjects: Bayesian data assimilation -- machine learning -- recurrent neural network -- ensemble‐based Kalman filtering; Geological modeling -- Periodicals; Climatology -- Periodicals; Geochemical modeling -- Periodicals; 551.5011
• DOI: 10.1029/2022MS003353
• Languages: English
• ISSNs: 1942-2466

Abstract

Abstract: Data Assimilation aims at estimating the posterior conditional probability density functions based on error statistics of the noisy observations and the dynamical system. State of the art methods are sub‐optimal due to the common use of Gaussian error statistics and the linearization of the non‐linear dynamics. To achieve a good performance, these methods often require case‐by‐case fine‐tuning by using explicit regularization techniques such as inflation and localization. In this paper, we propose a fully data driven deep learning framework generalizing recurrent Elman networks and data assimilation algorithms. Our approach approximates a sequence of prior and posterior densities conditioned on noisy observations using a log‐likelihood cost function . By construction our approach can then be used for general nonlinear dynamics and non‐Gaussian densities. As a first step, we evaluate the performance of the proposed approach by using fully and partially observed Lorenz‐95 system in which the outputs of the recurrent network are fitted to Gaussian densities. We numerically show that our approach, without using any explicit regularization technique, achieves comparable performance to the state‐of‐the‐art methods, IEnKF‐Q and LETKF, across various ensemble size. Plain Language Summary: Data Assimilation aims at forecasting the state of a dynamical system by combining information coming from the dynamics and noisy observations. Bayesian data assimilation uses the random nature of a system to predict its states in terms of probability density functions. The calculation of these densities is difficult for non‐linear dynamical systems. Practical algorithms compute limited statistics due to computational cost, but this results in sub‐optimal DA algorithms which requires then the use of explicit regularization techniques to increase the performance of the algorithm. With the advances in Machine Learning (ML) and deep learning, there has been significant increase in the research of using ML for data assimilation to decrease the computational cost, or to have better estimation of the state. In this paper, we propose a fully data driven algorithm to learn the prior and posterior pdfs conditioned on given observations. Our learning is based on a set of trajectories of the model and observations. It aims to correct the pdfs by optimizing likelihood‐based loss functions in the sense of the Kullback‐Leibler (KL) divergence. Numerical experiments show that we can obtain similar performance when compared with the IEnKF‐Q and LETKF methods, without the need of localization and inflation techniques. These numerical results shows the potential advantage of ML based algorithms when the used practical algorithms are sub‐optimal. Key Points: We propose a general framework Data Assimilation Networks (DAN) based on an extended Elman Network for Bayesian Data Assimilation We show that DAN can achieve optimal prior and posterior density estimations by optimizing likelihood‐based objective functions Numerically DAN achieve comparable performance to EnKF methods on Lorenz‐95 system, without using explicit regularization such as localization or inflation