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This paper investigates robust synchronization for multi-agent systems (MASs) governed by parabolic partial differential equations in the presence of both observable and unobservable disturbances. Using only boundary output measurements, a…

Systems and Control · Electrical Eng. & Systems 2026-05-20 Yongchun Bi , Jun Zheng , Guchuan Zhu , Jiye Zhang

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…

Optimization and Control · Mathematics 2010-11-29 L. Briceno-Arias , P. L. Combettes

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically…

Atmospheric and Oceanic Physics · Physics 2015-05-30 Jochen Bröcker , Ivan G. Szendro

This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved;…

Neural and Evolutionary Computing · Computer Science 2021-03-24 Elliot Meyerson , Risto Miikkulainen

This paper establishes strong convergence rates for the spatial finite element discretization of a two-dimensional stochastic Navier--Stokes system with transport noise and no-slip boundary conditions on a convex polygonal domain. The main…

Numerical Analysis · Mathematics 2025-12-15 Binjie Li , Qin Zhou

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

Chaotic Dynamics · Physics 2025-04-09 Max M. Chumley , Firas A. Khasawneh

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…

Atmospheric and Oceanic Physics · Physics 2012-12-17 Eugene Kazantsev

Given an undirected measurement graph $\mathcal{H} = ([n], \mathcal{E})$, the classical angular synchronization problem consists of recovering unknown angles $\theta_1^*,\dots,\theta_n^*$ from a collection of noisy pairwise measurements of…

Machine Learning · Statistics 2026-01-22 Ernesto Araya , Mihai Cucuringu , Hemant Tyagi

The shallow water equations (SWE) are a widely used model for the propagation of surface waves on the oceans. We consider the problem of optimally determining the initial conditions for the one-dimensional SWE in an unbounded domain from a…

Fluid Dynamics · Physics 2020-03-12 N. K. -R. Kevlahan , R. Khan , B. Protas

This paper improves the spectrally-filtered direct-insertion downscaling method for discrete-in-time data assimilation by introducing a relaxation parameter that overcomes a constraint on the observation frequency. Numerical simulations…

Numerical Analysis · Mathematics 2026-01-13 Emine Celik , Eric Olson

Satellite observations play a critical role in numerical weather prediction where they are assimilated through an observation operator that maps model states to radiances. In the traditional Ensemble Kalman Filter, these observations are…

Atmospheric and Oceanic Physics · Physics 2026-03-24 Gian Luca Buono , Stefanie Hollborn , Roland Potthast , Jörg Schäfer , Martin Simon

Data assimilation of observational data into full atmospheric states is essential for weather forecast model initialization. Recently, methods for deep generative data assimilation have been proposed which allow for using new input data…

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…

Machine Learning · Computer Science 2024-06-24 Matthieu Blanke , Ronan Fablet , Marc Lelarge

This report develops several modular, 2-step realizations (inspired by Kalman filter algorithms) of nudging-based data assimilation $$Step \ 1 \quad \frac{\widetilde {v}^{n+1}-v^{n}}{k}+v^{n}\cdot \nabla \widetilde {v}^{n+1}-\nu \triangle…

Numerical Analysis · Mathematics 2025-07-01 Aytekin Çıbık , Rui Fang , William Layton

In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal interpolation of multidimensional analytic functions defined over a product of one dimensional bounded domains. The goal of such approach is to…

Numerical Analysis · Mathematics 2015-08-06 Miroslav K. Stoyanov , Clayton G. Webster

In this paper we propose a continuous data assimilation (downscaling) algorithm for the B\'enard convection in porous media using only coarse mesh measurements of the temperature. In this algorithm, we incorporate the observables as a…

Analysis of PDEs · Mathematics 2015-10-12 Aseel Farhat , Evelyn Lunasin , Edriss S. Titi

Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…

Materials Science · Physics 2009-10-31 Ross A. Lippert , T. A. Arias , Alan Edelman

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…

Probability · Mathematics 2026-01-27 Kush Kinra

Hardware acceleration in modern networks creates monitoring blind spots by offloading flows to a non-observable state, hindering real-time service degradation (SD) detection. To address this, we propose and formalize a novel inter-flow…

Networking and Internet Architecture · Computer Science 2025-09-16 Balint Bicski , Adrian Pekar

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…

Numerical Analysis · Mathematics 2018-02-26 Daniele A. Di Pietro , Stella Krell