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Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low…
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman…
Quantifying forecast uncertainty is a key aspect of state-of-the-art numerical weather prediction and data assimilation systems. Ensemble-based data assimilation systems incorporate state-dependent uncertainty quantification based on…
We propose a generalised framework for the updating of a prior ensemble to a posterior ensemble, an essential yet challenging part in ensemble-based filtering methods. The proposed framework is based on a generalised and fully Bayesian view…
Global maps of the solar photospheric magnetic flux are fundamental drivers for simulations of the corona and solar wind and therefore are important predictors of geoeffective events. However, observations of the solar photosphere are only…
Detailed dynamical systems' models used in the life sciences may include hundreds of state variables and many input parameters, often with physical meaning. Therefore, efficient and unique input parameter identification, from experimental…
We introduce a computationally efficient variant of the model-based ensemble Kalman filter (EnKF). We propose two changes to the original formulation. First, we phrase the setup in terms of precision matrices instead of covariance matrices,…
Various methods have been proposed for the nonlinear filtering problem, including the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF), unscented Kalman filter (UKF) and iterated unscented Kalman filter (IUKF). In this…
The reconstruction of electrical excitation patterns through the unobserved depth of the tissue is essential to realizing the potential of computational models in cardiac medicine. We have utilized experimental optical-mapping recordings of…
This paper presents an approach for simultaneous estimation of the state and unknown parameters in a sequential data assimilation framework. The state augmentation technique, in which the state vector is augmented by the model parameters,…
In this work we determine key model parameters for rapidly intensifying Hurricane Guillermo (1997) using the Ensemble Kalman Filter (EnKF). The approach is to utilize the EnKF as a tool to only estimate the parameter values of the model for…
It is a grand challenge to find a feasible weather modification method to mitigate the impact of extreme weather events such as tropical cyclones. Previous works have proposed potentially effective actuators and assessed their capabilities…
We propose the use of the Extended Kalman Filter (EKF) for online data assimilation and update of a dynamic model, preliminary identified through the Sparse Identification of Nonlinear Dynamics (SINDy). This data-driven technique may avoid…
Artificial neural networks (ANNs) are widely used in modeling sentence processing but often exhibit deterministic behavior, contrasting with human sentence comprehension, which manages uncertainty during ambiguous or unexpected inputs. This…
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…
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…
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their widespread usage in climate science and…
Controlled interacting particle systems such as the ensemble Kalman filter (EnKF) and the feedback particle filter (FPF) are numerical algorithms to approximate the solution of the nonlinear filtering problem in continuous time. The…
The estimation from available data of parameters governing epidemics is a major challenge. In addition to usual issues (data often incomplete and noisy), epidemics of the same nature may be observed in several places or over different…