Related papers: Efficient Dynamical Downscaling of General Circula…
Obtaining accurate high-resolution representations of model outputs is essential to describe the system dynamics. In general, however, only spatially- and temporally-coarse observations of the system states are available. These observations…
We consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D Benard convection equations into a finer grid. In this CDA, a nudging term, estimated as the misfit…
This study assesses a Continuous Data Assimilation (CDA) dynamical-downscaling algorithm for enhancing the simulation of the Indian summer monsoon (ISM) system. CDA is a mathematically rigorous technique that has been recently introduced to…
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…
Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompressible flows, yet no physical flow is…
Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science. In practice, filtering methods rely on…
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…
The generation of initial conditions via accurate data assimilation is crucial for weather forecasting and climate modeling. We propose DiffDA as a denoising diffusion model capable of assimilating atmospheric variables using predicted…
Data assimilation (DA) is a fundamental component of modern weather prediction, yet it remains a major computational bottleneck in machine learning (ML)-based forecasting pipelines due to reliance on traditional variational methods. Recent…
Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's…
Continuous data assimilation (CDA) methods, such as the nudging algorithm introduced by Azouani, Olson, and Titi (AOT), have proven to be highly effective in deterministic settings for asymptotically synchronizing approximate solutions with…
This paper studies a coupled two-dimensional Navier--Stokes--Cahn--Hilliard phase-field model augmented by a transported auxiliary field, and develops a continuous data assimilation (CDA) framework for recovering its trajectories from…
Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has…
Using a very cheap Data Assimilation (DA) method, I show an alternative approach to classical DA for numerical climate models which produce a large amount of "big data". The problematic features of state-of-the-art high resolution Regional…
This paper improves the spectrally-filtered direct-insertion downscaling method for discrete-in-time data assimilation by introducing a relaxation parameter that overcomes a constraint on the observation frequency. Numerical simulations…
Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…
Data Assimilation (DA) plays a critical role in atmospheric science by reconstructing spatially continous estimates of the system state, which serves as initial conditions for scientific analysis. While recent advances in diffusion models…
Efficient downscaling of large ensembles of coarse-scale information is crucial in several applications, such as oceanic and atmospheric modeling. The determining form map is a theoretical lifting function from the low-resolution solution…
Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive…
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a…