Using machine learning to correct model error in data assimilation and forecast applications

Farchi, Alban; Laloyaux, Patrick; Bonavita, Massimo; Bocquet, Marc

doi:10.1002/qj.4116

Cited by 78 publications

(83 citation statements)

References 48 publications

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“…(2018). The other hybrid approaches of the same class use either a random forest (Watt‐Meyer et al., 2021) or use a deep learning ML component (Farchi et al., 2021), rather than one based on RC.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Approach to Atmospheric Modeling That Combines Machine Learning With a Physics‐Based Numerical Model

Arcomano

Szunyogh

Wikner

et al. 2022

J Adv Model Earth Syst

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This paper describes an implementation of the combined hybrid‐parallel prediction (CHyPP) approach of Wikner et al. (2020), https://doi.org/10.1063/5.0005541 on a low‐resolution atmospheric global circulation model (AGCM). The CHyPP approach combines a physics‐based numerical model of a dynamical system (e.g., the atmosphere) with a computationally efficient type of machine learning (ML) called reservoir computing to construct a hybrid model. This hybrid atmospheric model produces more accurate forecasts of most atmospheric state variables than the host AGCM for the first 7–8 forecast days, and for even longer times for the temperature and humidity near the earth's surface. It also produces more accurate forecasts than a model based only on ML, or a model that combines linear regression, rather than ML, with the AGCM. The potential of the CHyPP approach for climate research is demonstrated by a 10‐year long hybrid model simulation of the atmospheric general circulation, which shows that the hybrid model can simulate the general circulation with substantially smaller systematic errors and more realistic variability than the host AGCM.

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Section: Introductionmentioning

confidence: 99%

A Hybrid Approach to Atmospheric Modeling That Combines Machine Learning With a Physics‐Based Numerical Model

Arcomano

Szunyogh

Wikner

et al. 2022

J Adv Model Earth Syst

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“…In the geosciences, even though models are affected by errors (e.g., misrepresented physical phenomena, unresolved small-scale processes, numerical integration errors, etc), they benefit from a long history of modelling and therefore they already provide a solid baseline. For this reason, recent studies focus on using ML techniques for model error correction instead of full model emulation (Rasp et al, 2018;Bolton and Zanna, 2019;Jia et al, 2019;Watson, 2019;Bonavita and Laloyaux, 2020;Brajard et al, 2020b;Gagne et al, 2020;Wikner et al, 2020;Farchi et al, 2021). The idea is to build a hybrid model with a physical, knowledge-based part, and a statistical part to supplement it.…”

Section: Introduction: Machine Learning For Model Error Correctionmentioning

confidence: 99%

“…This means that the statistical model is trained to learn the error of the physical model. The underlying rationale is that model error correction should be an easier inference problem than full model emulation (Jia et al, 2019;Watson, 2019;Farchi et al, 2021).…”

Section: Introduction: Machine Learning For Model Error Correctionmentioning

confidence: 99%

“…A numerical scheme is used to integrate them for a small time step, and several integration steps are composed to define the resolvent between two forecast times. Following Farchi et al (2021), two strategies are possible for a correction term: (i) apply an integrated correction between two forecast times, i.e. in the resolvent, or (ii) apply a correction directly in the tendencies.…”

Section: Introduction: Machine Learning For Model Error Correctionmentioning

confidence: 99%

“…of the NN. The method has then been used to correct an imperfect physical model by Brajard et al (2020b); Farchi et al (2021). For this problem, the formalism is simply obtained by replacing the resolvent of the surrogate model M ∆t with the resolvent of the corrected model, in particular in eq.…”

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confidence: 99%

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A comparison of combined data assimilation and machine learning methods for offline and online model error correction

Farchi¹,

Bocquet²,

Laloyaux³

et al. 2021

Preprint

Self Cite

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Recent studies have shown that it is possible to combine machine learning methods with data assimilation to reconstruct a dynamical system using only sparse and noisy observations of that system. The same approach can be used to correct the error of a knowledge-based model. The resulting surrogate model is hybrid, with a statistical part supplementing a physical part. In practice, the correction can be added as an integrated term (i.e. in the model resolvent) or directly inside the tendencies of the physical model. The resolvent correction is easy to implement. The tendency correction is more technical, in particular it requires the adjoint of the physical model, but also more flexible. We use the two-scale Lorenz model to compare the two methods. The accuracy in long-range forecast experiments is somewhat similar between the surrogate models using the resolvent correction and the tendency correction. By contrast, the surrogate models using the tendency correction significantly outperform the surrogate models using the resolvent correction in data assimilation experiments. Finally, we show that the tendency correction opens the possibility to make online model error correction, i.e. improving the model progressively as new observations become available. The resulting algorithm can be seen as a new formulation of weak-constraint 4D-Var. We compare online and offline learning using the same framework with the two-scale Lorenz system, and show that with online learning, it is possible to extract all the information from sparse and noisy observations.

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Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

Masud,

Goraya

2024

Numerical Meth Engineering

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The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

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Using machine learning to correct model error in data assimilation and forecast applications

Cited by 78 publications

References 48 publications

A Hybrid Approach to Atmospheric Modeling That Combines Machine Learning With a Physics‐Based Numerical Model

A Hybrid Approach to Atmospheric Modeling That Combines Machine Learning With a Physics‐Based Numerical Model

A comparison of combined data assimilation and machine learning methods for offline and online model error correction

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

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