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This paper proposes an extension to the classical 3D variational data assimilation approach by explicitly incorporating as a prior information, the transform-domain sparsity observed in a large class of geophysical signals. In particular,…

Data Analysis, Statistics and Probability · Physics 2012-07-03 Ardeshir M. Ebtehaj , Efi Foufoula-Georgiou , Sara Q. Zhang , Arthur Y. Hou

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

Optimization and Control · Mathematics 2020-11-06 Shushu Zhang , Vivak Patel

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a non-abelian operator algebra, which provides a representation of…

Statistics Theory · Mathematics 2023-03-29 David Freeman , Dimitrios Giannakis , Brian Mintz , Abbas Ourmazd , Joanna Slawinska

Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…

Computation · Statistics 2015-03-19 Gabriel Terejanu , Puneet Singla , Tarunraj Singh , Peter D. Scott

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…

Methodology · Statistics 2023-11-01 Mengyang Gu , Yizi Lin , Victor Chang Lee , Diana Qiu

Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…

Fluid Dynamics · Physics 2025-02-25 Amirmoez Jamaat , Yalan Song , Farshid Rahmani , Jiangtao Liu , Kathryn Lawson , Chaopeng Shen

We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the…

Systems and Control · Electrical Eng. & Systems 2022-11-02 Wei Kang , Daniel M. Tartakovsky , Apoorv Srivastava

In the past couple of years, there is a proliferation in the use of machine learning approaches to represent subgrid scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical…

Computational Physics · Physics 2021-04-13 Suraj Pawar , Omer San

Fitting nonlinear dynamical models to sparse and noisy observations is fundamentally challenging. Identifying dynamics requires data assimilation (DA) to estimate system states, but DA requires an accurate dynamical model. To break this…

Machine Learning · Computer Science 2024-09-12 Vadim Zinchenko , David S. Greenberg

In this paper, we propose an uncertainty-aware learning from demonstration method by presenting a novel uncertainty estimation method utilizing a mixture density network appropriate for modeling complex and noisy human behaviors. The…

Computer Vision and Pattern Recognition · Computer Science 2018-12-21 Sungjoon Choi , Kyungjae Lee , Sungbin Lim , Songhwai Oh

Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in…

Signal Processing · Electrical Eng. & Systems 2025-06-06 Siyi Chen , Yixuan Jia , Qing Qu , He Sun , Jeffrey A Fessler

Data-driven methods have demonstrated strong predictive capabilities in fluid mechanics, yet most current applications still focus on simplified configurations, often characterised by statistical stationarity or limited temporal…

Fluid Dynamics · Physics 2025-11-21 Miguel M. Valero , Marcello Meldi

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple…

Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…

Analysis of PDEs · Mathematics 2018-12-06 Adam Larios , Collin Victor

Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science. In practice, filtering methods rely on…

Image and Video Processing · Electrical Eng. & Systems 2026-05-15 Yixuan Jia , Siyi Chen , Yida Pan , Xiao Li , Lianghe Shi , Chanyong Jung , Haijie Yuan , Ismail Alkhouri , Yue Cynthia Wu , Saiprasad Ravishankar , Jeffrey A Fessler , Qing Qu

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

Data Analysis, Statistics and Probability · Physics 2012-04-11 Lewis Mitchell , Georg A. Gottwald

In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…

Systems and Control · Electrical Eng. & Systems 2021-10-25 Loc Luong

Using a dynamical model to make predictions about a system has many sources of error. These can include errors in how the model was initialised but also errors in the dynamics of the model itself. For many applications in data assimilation,…

Numerical Analysis · Mathematics 2025-07-07 P. A. Browne

Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…

Methodology · Statistics 2018-04-19 Yen-Chi Chen , Y. Samuel Wang , Elena A. Erosheva

A framework for data assimilation combining aspects of operator-theoretic ergodic theory and quantum mechanics is developed. This framework adapts the Dirac--von Neumann formalism of quantum dynamics and measurement to perform sequential…

Mathematical Physics · Physics 2019-09-18 Dimitrios Giannakis