Related papers: Continuous Data Assimilation with a Moving Cluster…

High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two…

Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple…

This paper presents novel Gaussian process decentralized data fusion algorithms exploiting the notion of agent-centric support sets for distributed cooperative perception of large-scale environmental phenomena. To overcome the limitations…

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…

AI and data-driven models have large potential for data assimilation applications by creating fast and accurate forecasts. Their tendency to produce spurious inaccurate, nonphysical results -- hallucination -- however, raises a serious…

We show, using idealized models, that numerical data assimilation can be successful only if an effective dimension of the problem is not excessive. This effective dimension depends on the noise in the model and the data, and in physically…

Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses continuous data assimilation for a model arising as a…

Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our…

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…

We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…

With the development of Artificial Intelligence, numerous real-world tasks have been accomplished using technology integrated with deep learning. To achieve optimal performance, deep neural networks typically require large volumes of data…

The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic…

We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…

Data assimilation (DA) solves the inverse problem of inferring initial conditions given data and a model. Here we use biophysically motivated Hodgkin-Huxley (HH) models of avian HVCI neurons, experimentally obtained recordings of these…

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.…

These notes provide a systematic mathematical treatment of the subject of data assimilation.

In meteorological and oceanological studies the classical approach for finding the numerical solution of the regional model consists in formulating and solving the Cauchy-Dirichlet problem. The related boundary conditions are obtained by…

We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems…