Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations

Recent developments in machine learning (ML) have demonstrated impressive skills in reproducing complex spatiotemporal processes. However, contrary to data assimilation (DA), the underlying assumption behind ML methods is that the system is fully observed and without noise, which is rarely the case in numerical weather prediction. In order to circumvent this issue, it is possible to embed the ML problem into a DA formalism characterised by a cost function similar to that of the weak-constraint 4D-Var (Bocquet et al., 2019; Bocquet et al., 2020). In practice ML and DA are combined to solve the problem: DA is used to estimate the state of the system while ML is used to estimate the full model.&#160;In realistic systems, the model dynamics can be very complex and it may not be possible to reconstruct it from scratch. An alternative could be to learn the model error of an already existent model using the same approach combining DA and ML. In this presentation, we test the feasibility of this method using a quasi geostrophic (QG) model. After a brief description of the QG model model, we introduce a realistic model error to be learnt. We then asses the potential of ML methods to reconstruct this model error, first with perfect (full and noiseless) observation and then with sparse and noisy observations. We show in either case to what extent the trained ML models correct the mid-term forecasts. Finally, we show how the trained ML models can be used in a DA system and to what extent they correct the analysis.Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models, Nonlin. Processes Geophys., 26, 143&#8211;162, 2019Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization, Foundations of Data Science, 2 (1), 55-80, 2020Farchi, A., Laloyaux, P., Bonavita, M., and Bocquet, M.: Using machine learning to correct model error in data assimilation and forecast applications, arxiv:2010.12605, submitted.&#160;

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Model Reduction with Memory and the Machine Learning of Dynamical Systems

Communications in Computational Physics ◽

10.4208/cicp.oa-2018-0269 ◽

2019 ◽

Vol 25 (4) ◽

Cited By ~ 13

Author(s):

Chao Ma ◽

Jianchun Wang ◽

Weinan E

Keyword(s):

Machine Learning ◽

Dynamical Systems ◽

Model Reduction ◽

With Memory

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Comparison of the use of a physical-based model with data assimilation and machine learning methods for simulating soil water dynamics

Journal of Hydrology ◽

10.1016/j.jhydrol.2020.124692 ◽

2020 ◽

Vol 584 ◽

pp. 124692 ◽

Cited By ~ 2

Author(s):

Peijun Li ◽

Yuanyuan Zha ◽

Liangsheng Shi ◽

Chak-Hau Michael Tso ◽

Yonggen Zhang ◽

...

Keyword(s):

Machine Learning ◽

Data Assimilation ◽

Soil Water ◽

Water Dynamics ◽

Soil Water Dynamics ◽

Learning Methods ◽

Machine Learning Methods

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Synchronicity in predictive modelling: a new view of data assimilation

Nonlinear Processes in Geophysics ◽

10.5194/npg-13-601-2006 ◽

2006 ◽

Vol 13 (6) ◽

pp. 601-612 ◽

Cited By ~ 40

Author(s):

G. S. Duane ◽

J. J. Tribbia ◽

J. B. Weiss

Keyword(s):

Dynamical Systems ◽

Data Assimilation ◽

Ad Hoc ◽

Predictive Modelling ◽

Dimensional System ◽

General View ◽

Machine Perception ◽

Loosely Coupled ◽

Unidirectional Flow ◽

Observational Noise

Abstract. The problem of data assimilation can be viewed as one of synchronizing two dynamical systems, one representing "truth" and the other representing "model", with a unidirectional flow of information between the two. Synchronization of truth and model defines a general view of data assimilation, as machine perception, that is reminiscent of the Jung-Pauli notion of synchronicity between matter and mind. The dynamical systems paradigm of the synchronization of a pair of loosely coupled chaotic systems is expected to be useful because quasi-2D geophysical fluid models have been shown to synchronize when only medium-scale modes are coupled. The synchronization approach is equivalent to standard approaches based on least-squares optimization, including Kalman filtering, except in highly non-linear regions of state space where observational noise links regimes with qualitatively different dynamics. The synchronization approach is used to calculate covariance inflation factors from parameters describing the bimodality of a one-dimensional system. The factors agree in overall magnitude with those used in operational practice on an ad hoc basis. The calculation is robust against the introduction of stochastic model error arising from unresolved scales.

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