Related papers: Data Assimilation for Combined Parameter and State…
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…
In this paper, a dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the Particle Filtering (PF) scheme. Our developed methodology is based on a concurrent…
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…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
We introduce a framework for Data Assimilation (DA) in which the data is split into multiple sets corresponding to low-rank projections of the state space. Algorithms are developed that assimilate some or all of the projected data,…
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…
Algorithms for data assimilation try to predict the most likely state of a dynamical system by combining information from observations and prior models. Variational approaches, such as the weak-constraint four-dimensional variational data…
We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier-Stokes equations of fluid dynamics, are characterized…
Marine biogeochemistry models are critical for forecasting, as well as estimating ecosystem responses to climate change and human activities. Data assimilation (DA) improves these models by aligning them with real-world observations, but…
Continuous data assimilation (CDA) is a method that continuously integrates observational data into a dynamical system to improve model accuracy in real-time. The AOT algorithm is one of the most widely used methods in CDA due to its…
Assimilation of continuously streamed monitored data is an essential component of a digital twin; the assimilated data are used to ensure the digital twin is a true representation of the monitored system. One way this is achieved is by…
A large-scale, general-purpose data assimilation (DA) platform for materials modeling, douka, was developed and applied to nonlinear materials models. The platform demonstrated its effectiveness in estimating physical properties that cannot…
Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
State estimation of dynamical systems is crucial for providing new decision-making and system automation information in different applications. However, the assumptions on the standard computational models for sensor measurements can be…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…
We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is…
Continuous data assimilation (CDA) is successfully implemented for the first time for efficient dynamical downscaling of a global atmospheric reanalysis. A comparison of the performance of CDA with the standard grid and spectral nudging…
We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $\rho(v, t)$ given noisy observations of the true density…