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

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 state-of-the-art researches in this interdisciplinary field,covering a wide range of applications.This review is aimed 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.Index Terms-Data assimilation(DA),deep learning,machine learning(ML),reduced-order-modelling,uncertainty quantification(UQ).

Towards seamless environmental prediction-development of Pan-Eurasian EXperiment(PEEX)modelling platform

The Pan-Eurasian Experiment Modelling Platform(PEEX-MP)is one of the key blocks of the PEEX Research Programme.The PEEX MP has more than 30 models and is directed towards seamless envir-onmental prediction.The main focus area is the Arctic-boreal regions and China.The models used in PEEX-MP cover several main components of the Earth’s system,such as the atmosphere,hydrosphere,pedosphere and biosphere,and resolve the physicalchemicalbiological processes at different spatial and temporal scales and resolutions.This paper introduces and discusses PEEX MP multi-scale modelling concept for the Earth system,online integrated,forward/inverse,and socioeconomical modelling,and other approaches with a particular focus on applications in the PEEX geographical domain.The employed high-performance com-puting facilities,capabilities,and PEEX dataflow for modelling results are described.Several virtual research platforms(PEEXView,Virtual Research Environment,Web-based Atlas)for handling PEEX modelling and observational results are introduced.The over-all approach allows us to understand better physical-chemicalbiological processes,Earth’s system interactions and feedbacks and to provide valuable information for assessment studies on evaluating risks,impact,consequences,etc.for population,envir-onment and climate in the PEEX domain.This work was also one of the last projects of Prof.Sergej Zilitinkevich,who passed away on 15 February 2021.Since the finalization took time,the paper was actually submitted in 2023 and we could not argue that the final paper text was agreed with him.