Related papers: Data-assimilation by delay-coordinate nudging
Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…
Visual illusions provide a window into the mechanisms underlying visual processing, and dynamical neural circuit models offer a natural framework for proposing and testing theories of their emergence. We propose and analyze a delay-coupled…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…
Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…
This article develops a general framework for continuous deterministic data assimilation for semilinear parabolic equations by means of evolution equations. Introducing a nudged model driven by partial observations, the global…
Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a…
We propose, analyze, and test a novel continuous data assimilation reduced order model (DA-ROM) for simulating incompressible flows. While ROMs have a long history of success on certain problems with recurring dominant structures, they tend…
Anomaly detection in time series data is a critical challenge across various domains. Traditional methods typically focus on identifying anomalies in immediate subsequent steps, often underestimating the significance of temporal dynamics…
We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with…
Spiking Neural Networks (SNNs) are widely regarded as an energy-efficient paradigm for modeling and processing temporal and event-driven information. Incorporating delays in SNNs has been proven to be an effective mechanism for improving…
Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a…
Distributed optimization finds applications in large-scale machine learning, data processing and classification over multi-agent networks. In real-world scenarios, the communication network of agents may encounter latency that may affect…
We study different approaches to implementing sparse-in-time observations into the the Azouani-Olson-Titi data assimilation algorithm. We propose a new method which introduces a "data assimilation window" separate from the observational…
Coordinate descent methods usually minimize a cost function by updating a random decision variable (corresponding to one coordinate) at a time. Ideally, we would update the decision variable that yields the largest decrease in the cost…
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…
In this paper we propose a new sequential data assimilation method for non-linear ordinary differential equations with compact state space. The method is designed so that the Lyapunov exponents of the corresponding estimation error dynamics…
In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in…
In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local…
In this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback…