We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens' embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data.
CEREA（CEREA联合实验室）；École des Ponts ParisTech（巴黎高科桥路学校）；EDF R&D（法国电力集团研发中心）；ECMWF（欧洲中期天气预报中心）
The idea of using machine learning (ML) methods to reconstruct the dynamics of a system is the topic of recent studies in the geosciences, in which the key output is a surrogate model meant to emulate the dynamical model. In order to treat sparse and noisy observations in a rigorous way, ML can be combined to data assimilation (DA). This yields a class of iterative methods in which, at each iteration a DA step assimilates the observations, and alternates with a ML step to learn the underlying dynamics of the DA analysis. In this article, we propose to use this method to correct the error of an…
University of Maryland, College Park（马里兰大学帕克分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several promising data-driven approaches to forecasting of chaotic dynamical systems using machine learning. Particularly promising among these are hybrid approaches that combine machine learning with a knowledge-based model, where a machine-learning technique is used to correct the imperfections in the knowledge-based model. Such imperfections may be due to incomple…
Huracan: A skillful end-to-end data-driven system for ensemble data assimilation and weather prediction
Microsoft Corporation（微软公司）；Department of Earth System Science, Ministry of Education Key Laboratory for Earth System Modeling, Institute for Global Change Studies（教育部地球系统科学部门地球系统建模重点实验室，全球变化研究机构）；Tsinghua University（清华大学）
School of Mathematics and Statistics University of Sydney（悉尼大学数学与统计学院）；Institute of Mathematics University of Potsdam（波茨坦大学数学研究所）
Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of research data-assimilation has been successfully used to optimally combine forecast models and their inherent uncertainty with incoming noisy observations. The key idea in our work here is to achieve increased forecast capabilities by judiciously combining machine-learning algorithms and data assimilation. We combine the physics-agnostic data-driven approac…
Online machine-learning forecast uncertainty estimation for sequential data assimilation
Servicio Meteorológico Nacional（国家气象局）；Universidad de Buenos Aires（布宜诺斯艾利斯大学）；Instituto Franco-Argentino para el Estudio del Clima y sus Impactos (IRL 3351 IFAECI)（法阿气候及其影响研究所（IRL 3351 IFAECI））；Universidad Nacional del Nordeste（东北国立大学）；Centro de Investigaciones del Mar y la Atmósfera（海洋与大气研究中心）；IMT Atlantique（大西洋国立高等工业技术学院）；Inria（法国国家信息与自动化研究所）
PnP-DA: Towards Principled Plug-and-Play Integration of Variational Data Assimilation and Generative Models
Department of Earth and Environmental Engineering, Columbia University, New York, USA（哥伦比亚大学地球与环境工程系）；NSF Center for Learning the Earth with Artificial Intelligence and Physics (LEAP), New York, USA（国家科学基金会学习地球与人工智能和物理中心（LEAP））；Pasteur Labs, New York, USA（帕斯特实验室）；Courant Institute for Mathematical Science, New York University, New York, USA（纽约大学Courant数学科学研究所）
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Total E&P Research and Technology（道达尔勘探与生产研究和技术公司）；Energy & Environmental Research Center, University of North Dakota（北达科他大学能源与环境研究中心）
Fast assimilation of monitoring data to update forecasts of pressure buildup and carbon dioxide (CO2) plume migration under geologic uncertainties is a challenging problem in geologic carbon storage. The high computational cost of data assimilation with a high-dimensional parameter space impedes fast decision-making for commercial-scale reservoir management. We propose to leverage physical understandings of porous medium flow behavior with deep learning techniques to develop a fast history matching-reservoir response forecasting workflow. Applying an Ensemble Smoother Multiple Data Assimilatio…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；TotalEnergies E&P Research and Technology（道达尔能源勘探与生产研究技术中心）；University of North Dakota, Energy & Environmental Research Center（北达科他大学能源与环境研究中心）
Fast forecasting of reservoir pressure distribution in geologic carbon storage (GCS) by assimilating monitoring data is a challenging problem. Due to high drilling cost, GCS projects usually have spatially sparse measurements from wells, leading to high uncertainties in reservoir pressure prediction. To address this challenge, we propose to use low-cost Interferometric Synthetic-Aperture Radar (InSAR) data as monitoring data to infer reservoir pressure build up. We develop a deep learning-accelerated workflow to assimilate surface displacement maps interpreted from InSAR and to forecast dynami…
DAWP: A framework for global observation forecasting via Data Assimilation and Weather Prediction in satellite observation space
Shanghai Jiao Tong University（上海交通大学）；Fudan University（复旦大学）；The Chinese University of Hong Kong Shanghai AI Laboratory（香港中文大学上海人工智能实验室）；Shanghai AI Laboratory（上海人工智能实验室）
Nansen Environmental and Remote Sensing Center（南森环境与遥感中心）；Sorbonne Université（索邦大学）；Universitetet i Bergen（卑尔根大学）；Bjerknes Center for Climate Research（比耶克内斯气候研究中心）
Increasing the resolution of a model can improve the performance of a data assimilation system: first because model field are in better agreement with high resolution observations, then the corrections are better sustained and, with ensemble data assimilation, the forecast error covariances are improved. However, resolution increase is associated with a cubical increase of the computational costs. Here we are testing an approach inspired from images super-resolution techniques and called "Super-resolution data assimilation" (SRDA). Starting from a low-resolution forecast, a neural network (NN)…
Sorbonne University（索邦大学）；University of Reading（雷丁大学）；University of Utrecht（乌得勒支大学）；École des Ponts ParisTech（巴黎高科路桥学院）；EDF R&D（法国电力集团研发部）；Université Paris-Est（巴黎东大学）
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 ar…
Rice University（莱斯大学）；École Normale Supérieure（巴黎高等师范学院）；PSL University（巴黎文理研究大学）；California Institute of Technology（加州理工学院）
Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available from the system. Ensemble Kalman filter (EnKF) is a DA algorithm that is widely used in applications involving high-dimensional nonlinear dynamical systems. However, EnKF requires evolving large ensembles of forecasts using the dynamical model of the system. This often becomes computationally intractable, especially when the number of states of the system is v…
Cooperative Institute for Research in Environmental Sciences（环境科学合作研究所）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Physical Sciences Laboratory（物理科学实验室）；National Oceanic and Atmospheric Administration（美国国家海洋和大气管理局）；University of California San Diego（加州大学圣地亚哥分校）；Scripps Institution of Oceanography（斯克里普斯海洋研究所）
Data assimilation (DA) is integrated with machine learning in order to perform entirely data-driven online state estimation. To achieve this, recurrent neural networks (RNNs) are implemented as surrogate models to replace key components of the DA cycle in numerical weather prediction (NWP), including the conventional numerical forecast model, the forecast error covariance matrix, and the tangent linear and adjoint models. It is shown how these RNNs can be initialized using DA methods to directly update the hidden/reservoir state with observations of the target system. The results indicate that…
Google Research（谷歌研究院）；Technical University of Munich（慕尼黑工业大学）；Harvard University（哈佛大学）
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a cornerstone of large scale forecasting applications such as numerical weather prediction. As such, it is implemented in current operational systems of weather forecasting agencies across the globe. However, finding a good initial state poses a difficult optimization problem in part due to the non-invertible relationship between physical states and their correspo…
On conditional diffusion models for PDE simulations
University of Cambridge（剑桥大学）；Technical University of Denmark（丹麦技术大学）；Microsoft Research AI4Science（微软研究院AI4Science）；The Alan Turing Institute（艾伦·图灵研究所）
Accurate and Efficient Hybrid-Ensemble Atmospheric Data Assimilation in Latent Space with Uncertainty Quantification
Department of Earth and Environmental Engineering, School of Engineering and Applied Sciences, Climate School, Columbia University（地球与环境工程系，工程与应用科学学院，气候学院，哥伦比亚大学）；Learning the Earth with Artificial Intelligence and Physics (LEAP) Center, Columbia University（人工智能与物理学习地球中心，哥伦比亚大学）；Shanghai Artificial Intelligence Laboratory, Shanghai, China（上海人工智能实验室，上海，中国）；The Chinese University of Hong Kong, Hong Kong, China（香港中文大学，香港，中国）；Department of Computer Science and Technology, Tsinghua University, Beijing, China（计算机科学与技术系，清华大学，北京，中国）
The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions by systematically combining noisy, incomplete observations and numerical models of system dynamics to produce effective estimation schemes. We introduce amortized assimilation, a framework for learning to assimilate in dynamical systems from sequences of noisy observations with no need for ground truth data. We motivate the framework by extending powerful r…
