Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review

Abstract

Data Assimilation (DA) and Uncertainty quantification (UQ) are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics (CFD) to geoscience and climate systems. Recently, much effort has been given in combining DA, UQ and machine learning (ML) techniques. These research efforts seek to address some critical challenges in high-dimensional dynamical systems, including but not limited to dynamical system identification, reduced order surrogate modelling, error covariance specification and model error correction. A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains, resulting in the necessity for a comprehensive guide. This paper provides the first overview of the state-of-the-art researches in this interdisciplinary field, covering a wide range of applications. This review aims at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models, but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems. Therefore, this article has a special focus on how ML methods can overcome the existing limits of DA and UQ, and vice versa. Some exciting perspectives of this rapidly developing research field are also discussed.

Supermodeling: Improving Predictions with an Ensemble of Interacting Models

“…Modern ML methods have been used to bias correct models both offline (e.g., Chapman et al 2022) and online (Watt-Meyer et al 2021). Unless explicitly informed by physics (Cheng et al 2023;Jakhar et al 2023), ML models learn their knowledge about the climate, including basic physics, empirically from data alone. This learning task requires large amounts of data, even if training is restricted to connections leading to output units only, as in the "reservoir computing" approach (Schrauwen et al 2007).…”

On‐line machine‐learning forecast uncertainty estimation for sequential data assimilation

“…The use of ML techniques in the context of data assimilation have been discussed in several studies. The similarities between data assimilation and ML and their potential synergism has been introduced in Hsieh and Tang (1998) and reviewed in Cheng et al (2023). Bocquet et al (2019); Brajard et al (2020); Farchi et al (2021aFarchi et al ( , 2022 proposed a framework in which ML is used for the estimation of the system dynamics and to represent model errors, whereas data assimilation provides an on-line continuous optimization of the data-driven model.…”