Bilinear Residual Neural Network for the Identification and Forecasting of Geophysical Dynamics

Fablet, Ronan; Ouala, Said; Herzet, Cédric

doi:10.23919/eusipco.2018.8553492

Cited by 61 publications

(111 citation statements)

References 20 publications

(20 reference statements)

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“…Since the observations are "perfect", DA has not been carried out in this case. The RMSE-f at t 0 + h (see the right-most bar in panel (b)) is 0.014 which is close to the value in Fablet et al (2018) despite the fact that, in our case, the model is not identifiable. If the field is observed with less than 50% coverage, the skills are significantly degraded.…”

Section: Forecast Skillssupporting

confidence: 66%

“…As stated in the introduction, several papers have used convolutional neural networks for representing surrogate models (see, e.g., Shi et al, 2015;de Bezenac et al, 2017;Fablet et al, 2018). Equation (3) being in the incremental form x k+1 = x k + · · · , one-block residual networks are suitable (He et al, 2016).…”

Section: Convolutional Neural Network As Surrogate Modelmentioning

confidence: 99%

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Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model

Brajard

Carrassi

Bocquet

et al. 2019

Preprint

131

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A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting their future states. The method consists in applying iteratively a data assimilation step, here an ensemble Kalman filter, and a neural network. Data assimilation is used to optimally combine a surrogate model with sparse noisy data. The output analysis is spatially complete and is used as a training set by the neural network to update the surrogate model. The two steps are then repeated iteratively. Numerical experiments have been carried out using the chaotic 40-variables Lorenz 96 model, proving both convergence and statistical skills of the proposed hybrid approach. The surrogate model shows shortterm forecast skills up to two Lyapunov times, the retrieval of positive Lyapunov exponents as well as the more energetic frequencies of the power density spectrum. The sensitivity of the method to critical setup parameters is also presented: forecast skills decrease smoothly with increased observational noise but drops abruptly if less than half of the model domain is observed. The successful synergy between data assimilation and machine learning, proven here with a low-dimensional system, encourages further investigation of such hybrids with more sophisticated dynamics.

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Section: Forecast Skillssupporting

confidence: 66%

Section: Convolutional Neural Network As Surrogate Modelmentioning

confidence: 99%

Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model

Brajard

Carrassi

Bocquet

et al. 2019

Preprint

131

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show abstract

“…As opposed to the resolvent, unveiling the flow rate (4) may offer an explicit representation of the model, closer to an ordinary (or partial) differential equation system. This could be efficiently achieved through a simple expansion on monomial regressors [6] or using a NN [45,19,28]. It has been found that NN architectures for the dynamics that mimic numerical integration schemes, and which take the form of residual NNs, are particularly adequate [17,13].…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization

Bocquet¹,

Brajard²,

Carrassi³

et al. 2020

Foundations of Data Science

115

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The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has been suggested to combine data assimilation and machine learning in several ways. We show how to unify these approaches from a Bayesian perspective using expectation-maximization and coordinate descents. In doing so, the model, the state trajectory and model error statistics are estimated all together. Implementations and approximations of these methods are discussed. Finally, we numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.

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“…Several recent dynamical system identification techniques [14,15] can be used predict sp,t+1 from sp,t. Natural candidates to learn a parametrization of Φ are recurrent neural networks, such as LSTMs, which are able to handle long term temporal correlations.…”

Section: Neural Network Architectures To Learn Dynamical Systemsmentioning

confidence: 99%

Learning Endmember Dynamics in Multitemporal Hyperspectral Data Using A State-Space Model Formulation

Drumetz

Mura

Tochon

et al. 2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Self Cite

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Hyperspectral image unmixing is an inverse problem aiming at recovering the spectral signatures of pure materials of interest (called endmembers) and estimating their proportions (called abundances) in every pixel of the image. However, in spite of a tremendous applicative potential and the avent of new satellite sensors with high temporal resolution, multitemporal hyperspectral unmixing is still a relatively underexplored research avenue in the community, compared to standard image unmixing. In this paper, we propose a new framework for multitemporal unmixing and endmember extraction based on a state-space model, and present a proof of concept on simulated data to show how this representation can be used to inform multitemporal unmixing with external prior knowledge, or on the contrary to learn the dynamics of the quantities involved from data using neural network architectures adapted to the identification of dynamical systems.

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Bilinear Residual Neural Network for the Identification and Forecasting of Geophysical Dynamics

Cited by 61 publications

References 20 publications

Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model

Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model

Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization

Learning Endmember Dynamics in Multitemporal Hyperspectral Data Using A State-Space Model Formulation

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