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We give a finite-horizon variational formulation that places Bayesian filtering and smoothing, variational data assimilation, KL-regularized control, and Kalman-type methods inside one mathematically explicit hierarchy. For a discrete-time…
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…
The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…
This article shows that increasing the observation variance at small scales can reduce the ensemble size required to avoid collapse in particle filtering of spatially-extended dynamics and improve the resulting uncertainty quantification at…
Ensemble methods for classification and clustering have been effectively used for decades, while ensemble learning for outlier detection has only been studied recently. In this work, we design a new ensemble approach for outlier detection…
State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…
Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assigns to base models a set of deterministic, constant model weights that (1) do not fully account for variations in base model accuracy…
Data Assimilation (DA) is a computational tool that uses value from the model and the real measurement to arrive to an optimally acceptable value. Rather, this technique relies on the idea of Kalman gain. We point out that DA has two…
Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…
The Ensemble Kalman Inversion (EKI) method is widely used for solving inverse problems, leveraging ensemble-based techniques to iteratively refine parameter estimates. Despite its versatility, the accuracy of EKI is constrained by the…
Despite increasing popularity in empirical studies, the integration of machine learning generated variables into regression models for statistical inference suffers from the measurement error problem, which can bias estimation and threaten…
This document describes in detail a new hybrid ensemble-variational algorithm that generalizes existing ensemble or variational data assimilation approaches and would enable joint state/parameter estimations in ECMWF's Integrated…
Modern data analytics take advantage of ensemble learning and transfer learning approaches to tackle some of the most relevant issues in data analysis, such as lack of labeled data to use to train the analysis models, sparsity of the…
Variational Data Assimilation (DA) has been broadly used in engineering problems for field reconstruction and prediction by performing a weighted combination of multiple sources of noisy data. In recent years, the integration of deep…
The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general…
We propose a new 'Bi-Reduced Space' approach to solving 3D Variational Data Assimilation using Convolutional Autoencoders. We prove that our approach has the same solution as previous methods but has significantly lower computational…
Artificial ensemble inflation is a common technique in ensemble data assimilation, whereby the ensemble covariance is periodically increased in order to prevent deviation of the ensemble from the observations and possible ensemble collapse.…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase space dimension is typically much larger than the number of ensemble members which leads to inaccurate results in the computed…
In this work we propose an ensemble 4D seismic history matching framework for reservoir characterization. Compared to similar existing frameworks in reservoir engineering community, the proposed one consists of some relatively new…