Related papers: Spectral Filtering of Interpolant Observables for …
Variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…
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.…
This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…
We adapt a continuous data assimilation scheme, known as the Azouani-Olson-Titi (AOT) algorithm, to the case of moving observers for the 2D incompressible Navier-Stokes equations. We propose and test computationally several movement…
In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on…
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…
Accurate estimation of error covariances (both background and observation) is crucial for efficient observation compression approaches in data assimilation of large-scale dynamical problems. We propose a new combination of a covariance…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
This work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow…
The Gray--Scott model governs the interaction of two chemical species via a system of reaction-diffusion equations. Despite its simple form, it produces extremely rich patterns such as spots, stripes, waves, and labyrinths. That makes it…
We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural…
Adjoint-based data assimilation for turbulent Navier-Stokes flows is fundamentally limited by the behavior of the adjoint dynamics: in backward time, adjoint fields exhibit exponential growth and become increasingly dominated by small-scale…
This contribution introduces a novel signal extrapolation algorithm and its application to image error concealment. The signal extrapolation is carried out by iteratively generating a model of the signal suffering from distortion. Thereby,…
A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the…
Deep trackers have proven success in visual tracking. Typically, these trackers employ optimally pre-trained deep networks to represent all diverse objects with multi-channel features from some fixed layers. The deep networks employed are…
We present an approach to spectropolarimetry which requires neither moving parts nor time dependent modulation, and which offers the prospect of achieving high sensitivity. The technique applies equally well, in principle, in the optical,…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
Inferring the state and unknown parameters of a network of coupled oscillators is of utmost importance. This task is made harder when only partial and noisy observations are available, which is a typical scenario in realistic…