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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…
Today's ocean numerical prediction skills depend on the availability of in-situ and remote ocean observations at the time of the predictions only. Because observations are scarce and discontinuous in time and space, numerical models are…
This study evaluates a data assimilation framework based on reduced-order modeling (ROM-DA), complemented by a hybrid data-filling strategy, to reconstruct dynamic temperature fields in a phase-change-material (PCM) integrated solar chimney…
Recent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices…
Forecasting ocean drift trajectories are important for many applications, including search and rescue operations, oil spill cleanup and iceberg risk mitigation. In an operational setting, forecasts of drift trajectories are produced based…
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…
We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by…
Low-order thermoacoustic models are qualitatively correct, but they are typically quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low--order models quantitatively (more) accurate. First, we…
The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse of forecasting centers for over three decades. While this method provides a computationally…
We propose a new 'Bi-Reduced Space' approach to solving 3D Variational Data Assimilation using Convolutional Autoencoders. We prove that our approach has the same solution as previous methods but has significantly lower computational…
The spatio-temporal interpolation of large geophysical datasets has historically been addressed by Optimal Interpolation (OI) and more sophisticated equation-based or data-driven Data Assimilation (DA) techniques. Recent advances in the…
Accurate estimation of thermospheric mass density is a prerequisite for orbit prediction and space situational awareness, where the upper atmosphere responds nonlinearly to solar and geomagnetic forcing across several orders of magnitude.…
Weather forecasting is a crucial yet highly challenging task. With the maturity of Artificial Intelligence (AI), the emergence of data-driven weather forecasting models has opened up a new paradigm for the development of weather forecasting…
Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising throughout data science and computational science. One popular strategy for leveraging randomization is to use it…
We propose and analyze an inexact gradient method based on incremental proper orthogonal decomposition (iPOD) to address the data storage difficulty in time-dependent PDE-constrained optimization, particularly for a data assimilation…
Analyzing the validity and success of a data assimilation algorithm when some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for…
The forecasting skill of numerical weather prediction (NWP) models critically depends on the accurate initial conditions, also known as analysis, provided by data assimilation (DA). Traditional DA methods often face a trade-off between…
To improve the computational efficiency of heat transfer topology optimization, a Multigrid Assisted Reanalysis (MGAR) method is proposed in this study. The MGAR not only significantly improves the computational efficiency, but also…
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…
In applications such as free-space optical communication, a signal is often recovered after propagation through a turbulent medium. In this setting, it is common to assume that limited information is known about the turbulent medium, such…