Related papers: A Continuous-Time Ensemble Kalman-Bucy Smoother fo…

We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by…

Variational inference (VI) combined with Bayesian nonlinear filtering produces state-of-the-art results for latent time-series modeling. A body of recent work has focused on sequential Monte Carlo (SMC) and its variants, e.g., forward…

Continuous data assimilation (CDA) methods, such as the nudging algorithm introduced by Azouani, Olson, and Titi (AOT), have proven to be highly effective in deterministic settings for asymptotically synchronizing approximate solutions with…

We present a new adaptive particle-based data assimilation scheme for cryospheric applications that leverages promising developments in importance sampling. The proposed approach seeks to combine some of the advantages of two widely used…

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…

The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field…

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with…

Marine biogeochemistry models are critical for forecasting, as well as estimating ecosystem responses to climate change and human activities. Data assimilation (DA) improves these models by aligning them with real-world observations, but…

Data assimilation (DA) combines model forecasts and observations to estimate the optimal state of the atmosphere with its uncertainty, providing initial conditions for weather prediction and reanalyses for climate research. Yet, existing…

Enforcing sparse structure within learning has led to significant advances in the field of data-driven discovery of dynamical systems. However, such methods require access not only to time-series of the state of the dynamical system, but…

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…

A non-intrusive data assimilation methodology is developed to improve the statistical predictions of large-eddy simulations (LES). The ensemble-variational (EnVar) approach aims to minimize a cost function that is defined as the discrepancy…

A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…

Accurate post-processing navigation is essential for applications such as survey and mapping, where the full measurement history can be exploited to refine past state estimates. Fixed-interval smoothing algorithms represent the…

Causal inference is a fundamental research topic for discovering the cause-effect relationships in many disciplines. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to…

Ensemble learning is a standard approach to building machine learning systems that capture complex phenomena in real-world data. An important aspect of these systems is the complete and valid quantification of model uncertainty. We…

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman…

For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…

Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…