Related papers: FlowDAS: A Stochastic Interpolant-based Framework …

We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an…

Knowledge graph completion demands effective modeling of multifaceted semantic relationships between entities. Yet, prevailing methods, which rely on static scoring functions over learned embeddings, struggling to simultaneously capture…

Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

A thermal convection loop is a annular chamber filled with water, heated on the bottom half and cooled on the top half. With sufficiently large forcing of heat, the direction of fluid flow in the loop oscillates chaotically, dynamics…

We describe a spectrally-filtered discrete-in-time downscaling data assimilation algorithm and prove, in the context of the two-dimensional Navier--Stokes equations, that this algorithm works for a general class of interpolants, such as…

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…

Data assimilation (DA), as an indispensable component within contemporary Numerical Weather Prediction (NWP) systems, plays a crucial role in generating the analysis that significantly impacts forecast performance. Nevertheless, the…

The recent surge in machine learning (ML) methods for geophysical modeling has raised the question of how these methods might be applied to data assimilation (DA). We focus on diffusion modeling (a form of generative artificial…

Data assimilation (DA) is integrated with machine learning in order to perform entirely data-driven online state estimation. To achieve this, recurrent neural networks (RNNs) are implemented as surrogate models to replace key components of…

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,…

In atmospheric and turbulent flow modeling, Large Eddy Simulation (LES) is often used to reduce computational cost, while observational data typically originates from the underlying physical system. Motivated by this setting, we study a…

Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can…

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…

There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…

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…

We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the…

Accurate weather and climate prediction relies on data assimilation (DA), which estimates the Earth system state by integrating observations with models. While exascale computing has significantly advanced earth simulation, scalable and…

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…

In many practical scenarios, the dynamical system is not available and standard data assimilation methods are not applicable. Our objective is to construct a data-driven model for state estimation without the underlying dynamics. Instead of…