相关论文: Concurrent multi-parameter learning demonstrated o…

Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…

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…

Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…

We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…

In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary. On this…

In this study, we develop a continuous data assimilation algorithm to recover the parameter $\alpha$ in the simplified Bardina model. Our method utilizes the observations of finitely many Fourier modes by using a nudging framework that…

This article studies the intimate relationship between two filtering algorithms for continuous data assimilation, the synchronization filter and the nudging filter, in the paradigmatic context of the two-dimensional (2D) Navier-Stokes…

Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…

Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompressible flows, yet no physical flow is…

Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…

This paper demonstrates the applicability of the combination of concurrent learning as a tool for parameter estimation and non-parametric Gaussian Process for online disturbance learning. A control law is developed by using both techniques…

In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…

In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…

Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…

In this paper, a concurrent learning based adaptive observer is developed for a class of second-order nonlinear time-invariant systems with uncertain dynamics. The developed technique results in simultaneous online state and parameter…

We investigate a new sampling scheme aimed at improving the performance of particle filters whenever (a) there is a significant mismatch between the assumed model dynamics and the actual system, or (b) the posterior probability tends to…

State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…

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…

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is…

On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex…