Related papers: Variational Data Assimilation for Optimizing Bound…
Data assimilation (DA) integrates observational data with numerical models to improve the prediction of complex physical systems. However, traditional DA methods often struggle with nonlinear dynamics and multi-scale variability,…
We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with…
Particle filters are a group of algorithms to solve inverse problems through statistical Bayesian methods when the model does not comply with the linear and Gaussian hypothesis. Particle filters are used in domains like data assimilation,…
Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…
Global Climate Models are key tools for predicting the future response of the climate system to a variety of natural and anthropogenic forcings. Here we show how to use statistical mechanics to construct operators able to flexibly predict…
Estimating spatial extremes from sparse observational networks produces uncertain return level maps, but dense output from physics-based simulation models is often available as a complementary data source. We develop a two-stage frequentist…
Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…
Several advances have been made in Data Assimilation techniques applied to blood flow modeling. Typically, idealized boundary conditions, only verified in straight parts of the vessel, are assumed. We present a general approach, based on a…
Progress within physical oceanography has been concurrent with the increasing sophistication of tools available for its study. The incorporation of machine learning (ML) techniques offers exciting possibilities for advancing the capacity…
Assimilation of data into a fire-spread model is formulated as an optimization problem. The level set equation, which relates the fire arrival time and the rate of spread, is allowed to be satisfied only approximately, and we minimize a…
Understanding local currents in the North Atlantic region of the ocean is a key part of modelling heat transfer and global climate patterns. Satellites provide a surface signature of the temperature of the ocean with a high horizontal…
Ocean General Circulation Models require extensive computational resources to reach equilibrium states, while deep learning emulators, despite offering fast predictions, lack the physical interpretability and long-term stability necessary…
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…
Improving and optimizing oceanographic sampling is a crucial task for marine science and maritime resource management. Faced with limited resources in understanding processes in the water-column, the combination of statistics and autonomous…
We consider a new framework where a continuous, though bounded, random variable has unobserved bounds that vary over time. In the context of univariate time series, we look at the bounds as parameters of the distribution of the bounded…
A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…
Accurate and efficient global ocean state estimation remains a grand challenge for Earth system science, hindered by the dual bottlenecks of computational scalability and degraded data fidelity in traditional data assimilation (DA) and deep…
We consider a continuous data assimilation method for the barotropic Navier--Stokes system. The observed solution is supposed to be bounded on the whole time period of observation, while the synchronized solution, usually provided by a…
Variational inference (VI) combined with data subsampling enables approximate posterior inference over large data sets, but suffers from poor local optima. We first formulate a deterministic annealing approach for the generic class of…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…