Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional CFD application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.
In data assimilation, state estimation is not straightforward when the observation operator is unknown. This study proposes a method for composing a surrogate operator when the true operator is unknown. A neural network is used to improve the surrogate model iteratively to decrease the difference between the observations and the results of the surrogate model. A twin experiment suggests that the proposed method outperforms approaches that tentatively use a specific operator throughout the data assimilation process.
A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures, specifically a residual U-Net and a convolutional long short term memory recurrent network. Training samples entail global pressure and saturation maps, at a series of time steps, generated by simulating oil-water flow in many (1500 in our case) realizations of a 2D channelized system. After training, the `recurrent R-U-Net' surrogate model is shown to be capable of …
Virginia Tech（弗吉尼亚理工大学）；Oden Institute for Computational Engineering and Sciences, University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）
Data assimilation is the process of fusing information from imperfect computer simulations with noisy, sparse measurements of reality to obtain improved estimates of the state or parameters of a dynamical system of interest. The data assimilation procedures used in many geoscience applications, such as numerical weather forecasting, are variants of the our-dimensional variational (4D-Var) algorithm. The cost of solving the underlying 4D-Var optimization problem is dominated by the cost of repeated forward and adjoint model runs. This motivates substituting the evaluations of the physical model…
AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage
Faculty of Civil Engineering；Geosciences, TU Delft, Stevinweg 1, 2628 CN Delft, Netherlands；Centrum Wiskunde \& Informatica, Science Park 123, 1098 XG Amsterdam, Netherlands；Mathematical Institute, Utrecht University, Utrecht, Netherlands；Department of Earth Science；Engineering, Imperial College London, London, United Kingdom；Department of Energy Resources Engineering, Stanford University, CA, USA
CEREA, École des Ponts and EDF R&D（CEREA，巴黎高科桥梁学院与法国电力研发）；ECMWF（欧洲中期天气预报中心）
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 …
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…
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…
Virginia Tech（弗吉尼亚理工大学）；Computational Science Laboratory（计算科学实验室）
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities.…
EDF R&D（法国电力集团研发中心）；European Center for Research and Advanced Training in Scientific Computation (CERFACS)（欧洲科学计算高级研究与培训中心）；French National Research Center (CNRS)（法国国家科学研究中心）；Université de Toulouse（图卢兹大学）；Saint-Venant Laboratory for Hydraulics (LHSV)（圣维南水力学实验室）
Data assimilation (DA) is widely used to combine physical knowledge and observations. It is nowadays commonly used in geosciences to perform parametric calibration. In a context of climate change, old calibrations can not necessarily be used for new scenarios. This raises the question of DA computational cost, as costly physics-based numerical models need to be reanalyzed. Reduction and metamodelling represent therefore interesting perspectives, for example proposed in recent contributions as hybridization between ensemble and variational methods, to combine their advantages (efficiency, non-l…
Imperial College London（帝国理工学院）；University of Cambridge（剑桥大学）
There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that represent a dynamic system, is improved integrating real data coming from sensors using Data Assimilation techniques. In this paper, we formulate a new methodology called Latent Assimilation that combines Data Assimilation and Machine Learning. We use a Convolutional neural network to reduce the dimensionality of the problem, a Long-Short-Term-Memory to buil…
ANITI, Université de Toulouse（ANITI，图卢兹大学）；Atos BDS R&D AI4Sim（Atos BDS 研发 AI4Sim）；CERFACS（欧洲科学计算研究与高级培训中心）；UFTMIP；NVIDIA（英伟达）
Performing Data Assimilation (DA) at a low cost is of prime concern in Earth system modeling, particularly at the time of big data where huge quantities of observations are available. Capitalizing on the ability of Neural Networks techniques for approximating the solution of PDE's, we incorporate Deep Learning (DL) methods into a DA framework. More precisely, we exploit the latent structure provided by autoencoders (AEs) to design an Ensemble Transform Kalman Filter with model error (ETKF-Q) in the latent space. Model dynamics are also propagated within the latent space via a surrogate neural …
Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and the state-space dynamics are unknown. This paper introduces a machine learning framework for learning dynamical systems in data assimilation. Our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend ensemble Kalman filters for state recovery with machine learning tools for learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble …
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…
SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate
Department of Mechanical Engineering, Northwestern University, Evanston, IL, United States；Institute for Computational \& Mathematical Engineering, Stanford University, Stanford, CA, United States；Department of Industrial Engineering \& Management Sciences, Northwestern University, Evanston, IL, United States
Sparsely-Supervised Data Assimilation via Physics-Informed Schrödinger Bridge
Department of Industrial \& Systems Engineering, KAIST, Daejeon, Repulic of Korea；Department of Mathematical Sciences, KAIST, Daejeon, Repulic of Korea
Imperial College London（帝国理工学院）；Hong Kong University of Science and Technology（香港科技大学）；IMT Atlantique（大西洋国立高等工业、信息、航空与电信学院）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；École des Ponts（巴黎桥路学院）；EDF R&D（法国电力公司研发部）；Paris-Saclay University（巴黎萨克雷大学）；Electricité de France (EDF)（法国电力公司）；Sorbonne University（索邦大学）；Nansen Environmental and Remote Sensing Center (NERSC)（南森环境与遥感中心）；Tongji University（同济大学）；KU Eichstätt-Ingolstadt（艾希施泰特-因戈尔施塔特天主教大学）
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 an…
Modeling Partially Observed Nonlinear Dynamical Systems and Efficient Data Assimilation via Discrete-Time Conditional Gaussian Koopman Network
Department of Mechanical Engineering, University of Wisconsin–Madison（机械工程系，威斯康星大学麦迪逊分校）；Department of Mathematics, University of Wisconsin–Madison（数学系，威斯康星大学麦迪逊分校）
Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives
Laboratori de Càlcul Numeric (LaCàN), E.T.S. de Ingeniería de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya - BarcelonaTech (UPC)（计算数值实验室（LaCàN），土木工程系，加泰罗尼亚理工大学-巴塞罗那科技大学）；Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE)（国际数值工程方法中心）
The reconstruction of the dynamics of an observed physical system as a surrogate model has been brought to the fore by recent advances in machine learning. To deal with partial and noisy observations in that endeavor, machine learning representations of the surrogate model can be used within a Bayesian data assimilation framework. However, these approaches require to consider long time series of observational data, meant to be assimilated all together. This paper investigates the possibility to learn both the dynamics and the state online, i.e. to update their estimates at any time, in particu…
Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems
College of Information Sciences and Technology, Pennsylvania State University（宾夕法尼亚州立大学信息科学与技术学院）；School of Mechanical Engineering, Purdue University（普渡大学机械工程学院）
Graphical conditional generative modeling for digital twin modeling
Department of Computing and Mathematical Sciences, California Institute of Technology（计算与数学科学系，加州理工学院）；Department of Statistical Sciences, University of Toronto（统计科学系，多伦多大学）
Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations
School of Computational Science and Engineering, Georgia Institute of Technology（计算科学与工程学院，佐治亚理工学院）；Environmental Science Division, Argonne National Laboratory（环境科学部，阿贡国家实验室）
Department of Mathematics, Emory University（埃默里大学数学系）；School of Mathematical and Statistical Sciences, Clemson University（克林斯敦大学数学与统计科学学院）；Argonne National Laboratory（阿贡国家实验室）
