Related papers: Spectral Filtering of Interpolant Observables for …
This paper considers improving the Picard and Newton iterative solvers for the Navier-Stokes equations in the setting where data measurements or solution observations are available. We construct adapted iterations that use continuous data…
In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function…
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…
This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
Recently a new adaptive path interpolation method has been developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random…
Collaborative filtering is a popular approach in recommender systems, whose objective is to provide personalized item suggestions to potential users based on their purchase or browsing history. However, personalized recommendations require…
This study demonstrates how the incremental 4D-Var data assimilation method can be applied efficiently preconditione d in an application to an oceanographic problem. The approach consists in performing a few iterations of the reduced-order…
In this study, a perceptually hidden object-recognition method is investigated to generate secure images recognizable by humans but not machines. Hence, both the perceptual information hiding and the corresponding object recognition methods…
In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
An interpolation method for discretising continuous-time Linear Time Invariant (LTI) models is proposed in this paper. It consists first in using the Loewner interpolation framework on a specific set of frequency data and secondly to…
We present a simple algorithm for detecting oscillatory behavior in discrete data. The data is used as an input driving force acting on a set of simulated damped oscillators. By monitoring the energy of the simulated oscillators, we can…
We propose deep parameter interpolation (DPI), a general-purpose method for transforming an existing deep neural network architecture into one that accepts an additional scalar input. Recent deep generative models, including diffusion…
The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…
The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…
This paper studies a coupled two-dimensional Navier--Stokes--Cahn--Hilliard phase-field model augmented by a transported auxiliary field, and develops a continuous data assimilation (CDA) framework for recovering its trajectories from…
Suppose $L$ simultaneous independent stochastic systems generate observations, where the observations from each system depend on the underlying parameter of that system. The observations are unlabeled (anonymized), in the sense that an…
Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…