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Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous…
In many real-world applications of data assimilation (DA), the strategic placement of observers is crucial for effective and efficient forecasting. Motivated by practical constraints in sensor deployment, we show that global recovery of the…
We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…
Data assimilation techniques are crucial for accurately tracking complex dynamical systems by integrating observational data with numerical forecasts. Recently, score-based data assimilation methods emerged as powerful tools for…
We discuss the discrete data assimilation problem for the 3D viscous primitive equations arising in the modeling of large scale phenomena in oceanic dynamics. Our main result states possibility of asymptotically reliable prognosis based on…
The Picard iteration for the Boussinesq model of natural convection can be an attractive solver because it stably decouples the fluid equations from the temperature equation (for contrast, the Newton iteration does not stably decouple).…
We provide a new algorithmic framework for differentially private estimation of general functions that adapts to the hardness of the underlying dataset. We build upon previous work that gives a paradigm for selecting an output through the…
Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses first and second order adjoint sensitivity analysis, together…
Differential privacy comes equipped with multiple analytical tools for the design of private data analyses. One important tool is the so-called "privacy amplification by subsampling" principle, which ensures that a differentially private…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
The process monitoring task is characterized by stringent demands for accuracy and efficiency. Current transformer-based methods, characterized by self-attention for temporal fusion, exhibit limitations in accurately understanding the…
Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data…
In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis to decompose the signal is not…
We propose, analyze, and test a novel continuous data assimilation two-phase flow algorithm for reservoir simulation. We show that the solutions of the algorithm, constructed using coarse mesh observations, converge at an exponential rate…
In a recent paper, Hou and Shi introduced a new adaptive data analysis method to analyze nonlinear and non-stationary data. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary…
Fixed effect estimators of nonlinear panel data models suffer from the incidental parameter problem. This leads to two undesirable consequences in applied research: (1) point estimates are subject to large biases, and (2) confidence…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general…