A list of literature that we find useful for Data Assimilation.
Could be moved to docs/source eventually.
An optimization approach.
The observations are perturbed once, and we use the Gauss-Newton algorithm to minimize a cost function.
The proposed algorithm has state across iterations in a matrix
- (2019) Efficient Implementation of an Iterative Ensemble Smoother for Data Assimilation and Reservoir History Matching by Evensen et al
The idea behind ESMDA is to inflate the covariance of the observations and update several times. In the Gauss-Linear case, this makes no difference. The hope is that for non-linear forward models, it's better to make many small updates rather than one big update. Just like with SIES, there are no theoretical guarantees. One difference between ESMDA and SIES is that ESMDA perturbs in each iteration, whereas SIES perturbs once. The 2013 paper is the main paper, but the others are related too.
- (2012) History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations by Emerick et al
- (2013) Ensemble smoother with multiple data assimilation by Emerick et al
- (2016) An Adaptive Ensemble Smoother With Multiple Data Assimilation for Assisted History Matching by Emerick et al
Some papers that might be useful to have a look at.
- (2012) Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification by Chen et al
- (2014) Randomize-Then-Optimize: A Method for Sampling from Posterior Distributions in Nonlinear Inverse Problems by Bardsley et al
- (2018) Analysis of iterative ensemble smoothers for solving inverse problems by Evensen
- (2023) Review of ensemble gradients for robust optimisation by Raanes et al
- (2014) Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings by Touloumis
- (2022) GraphSPME: Markov Precision Matrix Estimation and Asymptotic Stein-Type Shrinkage by Lunde et al
- (unpublished) An Ensemble Information Filter: Retrieving Markov-Information from the SPDE discretization by Lunde et al
- (2022) Ensemble transport smoothing. Part I: Unified framework by Ramgraber et al
- (2022) Ensemble transport smoothing. Part II: Nonlinear updates by Ramgraber et al
- (2006) Pattern Recognition and Machine Learning by Bishop
- In particular, see Section 2.3.3: Bayes' theorem for Gaussian variables
- (2014) Data Assimilation: The Ensemble Kalman Filter by Evensen
- (2022) Data Assimilation Fundamentals: A Unified Formulation of the State and Parameter Estimation Problem by Evensen