Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems: A Review

Cheng, Sibo; Quilodrán-Casas, César; Ouala, Said; Farchi, Alban; Fablet, Ronan; Lucor, Didier; Iooss, Bertrand; Brajard, Julien; Xiao, Dunhui; Janjić, Tijana; Ding, Weiping; Guo, Yike; Carrassi, Alberto; Bocquet, Marc; Arcucci, Rossella

doi:10.1109/jas.2023.123537

Cited by 63 publications

(17 citation statements)

References 239 publications

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“…In recent years, the integration of ML, DA, and uncertainty quantification has demonstrated promising outcomes in enhancing the accuracy and comprehension of models in diverse fields (Cheng et al., 2023). Our work builds on the growing literature describing ML‐based methods for learning and aiding the DA processes.…”

Section: Related Workmentioning

confidence: 99%

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A Four‐Dimensional Variational Constrained Neural Network‐Based Data Assimilation Method

Wang,

Ren,

Duan

et al. 2024

J Adv Model Earth Syst

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Advances in data assimilation (DA) methods and the increasing amount of observations have continuously improved the accuracy of initial fields in numerical weather prediction during the last decades. Meanwhile, in order to effectively utilize the rapidly increasing data, Earth scientists must further improve DA methods. Recent studies have introduced machine learning (ML) methods to assist the DA process. In this paper, we explore the potential of a four‐dimensional variational (4DVar) constrained neural network (NN) method for accurate DA. Our NN is trained to approximate the solution of the variational problem, thereby avoiding the need for expensive online optimization when generating the initial fields. In the context that the full‐field system truths are unavailable, our approach embeds the system's kinetic features described by a series of analysis fields into the NN through a 4DVar‐form loss function. Numerical experiments on the Lorenz96 physical model demonstrate that our method can generate better initial fields than most traditional DA methods at a low computational cost, and is robust when assimilating observations with higher error outside of the distributions where it is trained. Furthermore, our NN‐based DA model is effective against Lorenz96 physical models with larger variable numbers. Our approach exemplifies how ML methods can be leveraged to improve both the efficiency and accuracy of DA techniques.

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Section: Related Workmentioning

confidence: 99%

“…Further, Bocquet (2023) and Cheng et al. (2023) highlight the potential of ML and DA for improving the accuracy and efficiency of models in Earth sciences. In addition, the synergy between ML and DA has been highlighted by Boukabara et al.…”

Section: Introductionmentioning

confidence: 99%

A Four‐Dimensional Variational Constrained Neural Network‐Based Data Assimilation Method

Wang,

Ren,

Duan

et al. 2024

J Adv Model Earth Syst

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“…This process is commonly regarded as parameter estimation problems, which have been addressed by Kalman filters (Qian et al, 2022), Particle filters (Eftekhar Azam and Mariani, 2018), and Bayesian estimation (Yuen and Kuok, 2011) and their various derivatives. Associated research areas include data assimilation (Cheng et al, 2023) and hybrid simulation (Al-Subaihawi et al, 2022). Although these online update methods have been applied successfully in fields such as structure health monitoring, agriculture, and fluid dynamics, the update formulas are designed based on the system's PDEs, rendering them inapplicable to scenarios where the PDEs are unknown.…”

Section: Literature Reviewmentioning

confidence: 99%

A Systematic Online Update Method for Reduced-Order-Model-Based Digital Twin

Tang,

Sajadi,

Dehaghani

et al. 2024

Preprint

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A digital twin (DT) is a model that mirrors a physical system and is continuously updated with real-time data from the physical system. Recent implementations of reduced-order-model-based DT (DT-ROM) have been applied in aerodynamics and structural health monitoring, where partial differential equations (PDEs) are utilized to update reduced bases and coefficients. However, these methods are not directly applicable when the PDEs of the system are unknown. This paper addresses the online update challenge for DT-ROM in scenarios lacking known PDEs of the system. To tackle the challenge, a systematic online update and application method is proposed. During the online update, the projection residual of online data on the reduced bases determines the necessity of updating reduced bases, while the prediction residual of online data obtained by the current DT-ROM is used to decide whether to update the coefficient model. By sequentially evaluating both criteria, the method selectively incorporates essential online data for the online DT model update. During the online application, a criterion defined based on online data is adopted to determine whether the offline DT-ROM or the online one is applied to output final predictions. The capability of the proposed method is tested through three numerical and three engineering problems. Results indicate that the proposed online update method consistently reduces both projection and prediction residuals, thereby progressively enhancing the performance of the online DT-ROM on test data. Meanwhile, the online application method provides a prediction performance better than using offline DT-ROM only. Both demonstrate that the proposed work could be applied to online DT update where the PDEs of the system are unknown.

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“…Reducing these model errors through improving the fundamental understanding of these processes and increasing the numerical resolution has been the subject of extensive past and ongoing efforts (Bonavita & Laloyaux, 2020; Danforth & Kalnay, 2008; Dunbar et al., 2021; Regayre et al., 2023). More recently, the rapid rise in the availability of high‐quality, frequent observations and algorithmic advances, particularly in data assimilation (DA) and machine learning (ML) (Cheng et al., 2023), can provide another promising direction for reducing such model errors and the resulting biases and uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Interpretable Structural Model Error Discovery From Sparse Assimilation Increments Using Spectral Bias‐Reduced Neural Networks: A Quasi‐Geostrophic Turbulence Test Case

Mojgani,

Chattopadhyay,

Hassanzadeh

2024

J Adv Model Earth Syst

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Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi‐scale processes, leading to uncertainties in their long‐term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short‐term simulations, for example, as differences between the predicted and observed states (analysis increments). With the increase in the availability of high‐quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data‐hungry, and poorly generalize out‐of‐distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data‐efficient framework that uses sparsity‐promoting equation‐discovery techniques to learn model errors from analysis increments. Using two‐layer quasi‐geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

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Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems: A Review

Cited by 63 publications

References 239 publications

A Four‐Dimensional Variational Constrained Neural Network‐Based Data Assimilation Method

A Four‐Dimensional Variational Constrained Neural Network‐Based Data Assimilation Method

A Systematic Online Update Method for Reduced-Order-Model-Based Digital Twin

Interpretable Structural Model Error Discovery From Sparse Assimilation Increments Using Spectral Bias‐Reduced Neural Networks: A Quasi‐Geostrophic Turbulence Test Case

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