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 build a surrogate model of the dynamic system and an Optimal Interpolated Kalman Filter to incorporate real data. Experimental results are provided for CO2 concentration within an indoor space. This methodology can be used for example to predict in real-time the load of virus, such as the SARS-COV-2, in the air by linking it to the concentration of CO2.
Latent assimilation with implicit neural representations for unknown dynamics
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Beijing International Center for Mathematical Research, Peking University（北京国际数学研究中心）；Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）；School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
Imperial College London（帝国理工学院）；University College London（伦敦大学学院）
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. T…
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 …
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）
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）
College of Information Science and Engineering, China University of Petroleum – Beijing（中国石油大学（北京）信息科学与工程学院）
In recent years, the prosperity of deep learning has revolutionized the Artificial Neural Networks. However, the dependence of gradients and the offline training mechanism in the learning algorithms prevents the ANN for further improvement. In this study, a gradient-free training framework based on data assimilation is proposed to avoid the calculation of gradients. In data assimilation algorithms, the error covariance between the forecasts and observations is used to optimize the parameters. Feedforward Neural Networks (FNNs) are trained by gradient decent, data assimilation algorithms (Ensem…
Imperial College London（伦敦帝国理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；EDF R&D（法国电力公司研发部）
Data assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modelling is an important element in data assimilation algorithms which can considerably impact the forecasting accuracy. The estimation of these covariances, which usually relies on empirical assumptions and physical constraints, is often imprecise and computationally expensive especially for systems of large dimension. In this work, we propose a data-driven approach based on long short term memory (LSTM) recurrent neural networ…
Pacific Northwest National Laboratory（太平洋西北国家实验室）；INTERA Incorporated（INTERA公司）
Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a physics-informed deep neural networks (DNNs) machine learning method for estimating space-dependent hydraulic conductivity, hydraulic head, and concentration fields from sparse measurements. In this approach, we employ individual DNNs to approximate the unknown parameters (e.g., hydraulic conductivity) and states (e.g., hydraulic head…
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…
Data assimilation and discrepancy modeling with shallow recurrent decoders
Department of Applied Mathematics, University of Washington（应用数学系，华盛顿大学）；Department of Electrical and Computer Engineering, University of Washington（电气与计算机工程系，华盛顿大学）
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.
Differential equations play a pivotal role in modern world ranging from science, engineering, ecology, economics and finance where these can be used to model many physical systems and processes. In this paper, we study two mathematical models of a drug assimilation in the human system using Physics Informed Neural Networks (PINNs). In the first model, we consider the case of single dose of drug in the human system and in the second case, we consider the course of this drug taken at regular intervals. We have used the compartment diagram to model these cases. The resulting differential equation…
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…
Meta-Learning Fourier Neural Operators for Hessian Inversion and Enhanced Variational Data Assimilation
School of Computational Science and Engineering, McMaster University（计算科学与工程学院，麦斯特大学）；Mathematics and Statistics, McMaster University（数学与统计学，麦斯特大学）；Department of Chemistry and Chemical Biology, McMaster University（化学与生物化学系，麦斯特大学）
本文提出元学习 FNO 框架近似跨 DA 问题的逆 Hessian，以初始化 CG；线性平流实验显示 FNO-CG 显著降低误差与迭代数，尤其适用于病态场景。
Marine Physical Laboratory (Scripps Institution of Oceanography), University of California, San Diego（加州大学圣迭戈分校斯克里普斯海洋研究所海洋物理实验室）；Department of Physics, University of California, San Diego（加州大学圣迭戈分校物理系）
We identify a strong equivalence between neural network based machine learning (ML) methods and the formulation of statistical data assimilation (DA), known to be a problem in statistical physics. DA, as used widely in physical and biological sciences, systematically transfers information in observations to a model of the processes producing the observations. The correspondence is that layer label in the ML setting is the analog of time in the data assimilation setting. Utilizing aspects of this equivalence we discuss how to establish the global minimum of the cost functions in the ML context,…
Interpretable Diagnostics and Adaptive Data Assimilation for Neural ODEs via Discrete Empirical Interpolation
School of Mechanical Engineering, Purdue University（普渡大学机械工程学院）；Mathematics and Computer Science Division, Argonne National Laboratory（阿贡国家实验室数学与计算机科学部）
University of Sydney（悉尼大学）；University of Potsdam（波茨坦大学）
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.
This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the NN models using b…
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…
Physics-informed neural networks for phase-resolved data assimilation and prediction of nonlinear ocean waves
Hamburg University of Technology（汉堡工业大学）；Imperial College London（帝国理工学院）；University of Oxford（牛津大学）；Universitat Politécnica de Catalunya（加泰罗尼亚理工大学）；China University of Petroleum（中国石油大学）；College of Oceanography（海洋学院）；Space Informatics（空间信息学院）
Data assimilation and parameter identification for water waves using the nonlinear Schrödinger equation and physics-informed neural networks
Hamburg University of Technology（汉堡工业大学）；TU Dortmund University（多特蒙德工业大学）；Technical University of Munich（慕尼黑工业大学）；German Aerospace Center（德国航空航天中心）；Imperial College London（伦敦帝国理工学院）；Technische Universität Berlin（柏林工业大学）
PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems
Hong Kong University of Science and Technology (Guangzhou)（香港理工大学（广州））；Hong Kong University of Science and Technology（香港理工大学）；Shandong University（山东大学）；University of Oxford（牛津大学）
Mean flow data assimilation using physics-constrained Graph Neural Networks
Dipartimento di Meccanica, Matematica e Management Politecnico di Bari（巴里理工学院机械、数学与管理系）；LISN-CNRS Université Paris-Saclay（巴黎萨克雷大学LISN-CNRS）；Digital Sciences & Technologies Department SafranTech（SafranTech数字科学与技术部门）
本文提出将 RANS 伴随梯度作为物理约束嵌入 GNN 训练，并结合 FEM 处理非结构化 CFD 数据，以在稀疏、含噪或缺损条件下提升钝体平均流重建精度。
