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Data Augmentation (DA) is a technique to increase the quantity and diversity of the training data, and by that alleviate overfitting and improve generalisation. However, standard DA produces synthetic data for augmentation with limited…

Computer Vision and Pattern Recognition · Computer Science 2023-07-24 Lorenzo Tronchin , Minh H. Vu , Paolo Soda , Tommy Löfstedt

Accurate data assimilation (DA) for systems with piecewise-smooth or discontinuous state variables remains a significant challenge, as conventional covariance-based ensemble Kalman filter approaches often fail to effectively balance…

Numerical Analysis · Mathematics 2025-10-09 Tongtong Li , Anne Gelb , Yoonsang Lee

This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic…

Computational Physics · Physics 2021-11-10 Ronan Fablet , Bertrand Chapron , Lucas. Drumetz , Etienne Memin , Olivier Pannekoucke , Francois Rousseau

The data-aware method of distributions (DA-MD) is a low-dimension data assimilation procedure to forecast the behavior of dynamical systems described by differential equations. It combines sequential Bayesian update with the MD, such that…

Statistics Theory · Mathematics 2022-07-27 Francesca Boso , Daniel M. Tartakovsky

We investigate how symmetries present in datasets affect the structure of the latent space learned by Variational Autoencoders (VAEs). By training VAEs on data originating from simple mechanical systems and particle collisions, we analyze…

Machine Learning · Computer Science 2025-04-08 Veronica Sanz

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework…

Machine Learning · Computer Science 2026-02-18 Francisco Giral , Álvaro Manzano , Ignacio Gómez , Ricardo Vinuesa , Soledad Le Clainche

Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operators whose functional forms are typically assumed to be…

Machine Learning · Statistics 2024-07-25 Alex Glyn-Davies , Connor Duffin , Ö. Deniz Akyildiz , Mark Girolami

A method of data assimilation (DA) is employed to estimate electrophysiological parameters of neurons simultaneously with their synaptic connectivity in a small model biological network. The DA procedure is cast as an optimization, with a…

Neurons and Cognition · Quantitative Biology 2020-02-05 Eve Armstrong

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…

Machine Learning · Statistics 2020-03-31 Marc Bocquet , Julien Brajard , Alberto Carrassi , Laurent Bertino

Data Assimilation (DA) has enabled huge improvements in the skill of terrestrial operational weather forecasting. In this study, we use a variational DA scheme with a computationally efficient solar wind model and in situ observations from…

Space Physics · Physics 2021-08-04 Matthew Lang , Jake Witherington , Harriet Turner , Matt Owens , Pete Riley

Data assimilation (DA) for systems governed by partial differential equations (PDE) aims to reconstruct full spatiotemporal fields from sparse high-fidelity (HF) observations while respecting physical constraints. While full-grid…

Machine Learning · Computer Science 2026-03-25 Dohyun Bu , Chanho Kim , Seokun Choi , Jong-Seok Lee

Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range…

Machine Learning · Computer Science 2025-11-18 Amirpasha Hedayat , Karthik Duraisamy

Discrete latent spaces in variational autoencoders have been shown to effectively capture the data distribution for many real-world problems such as natural language understanding, human intent prediction, and visual scene representation.…

Machine Learning · Computer Science 2021-01-19 Masha Itkina , Boris Ivanovic , Ransalu Senanayake , Mykel J. Kochenderfer , Marco Pavone

Representation learning has proven to be a powerful methodology in a wide variety of machine learning applications. For atmospheric dynamics, however, it has so far not been considered, arguably due to the lack of large-scale, labeled…

Atmospheric and Oceanic Physics · Physics 2022-08-24 Sebastian Hoffmann , Christian Lessig

We present a new method to visualize data ensembles by constructing structured probabilistic representations in latent spaces, i.e., lower-dimensional representations of spatial data features. Our approach transforms the spatial features of…

Machine Learning · Computer Science 2025-09-17 Cenyang Wu , Qinhan Yu , Liang Zhou

Analyzing the validity and success of a data assimilation algorithm when some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for…

Analysis of PDEs · Mathematics 2016-08-18 Aseel Farhat , Evelyn Lunasin , Edriss S. Titi

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

Data Analysis, Statistics and Probability · Physics 2012-04-11 Lewis Mitchell , Georg A. Gottwald

This paper addresses the impact of assimilating data from the Earth Networks Total Lightning Network (ENTLN) during two cases of severe weather. Data from the ENTLN serve as a substitute for those from the upcoming launch of the GOES…

Optimization and Control · Mathematics 2013-06-11 Razvan Stefanescu , I. Michael Navon , Henry Fuelberg , Max Marchand

Micrometeorology, city comfort, land use management and air quality monitoring increasingly become important environmental issues. To serve the needs, meteorology needs to achieve a serious advance in representation and forecast on…

Atmospheric and Oceanic Physics · Physics 2010-02-09 Igor Esau

Diffusion autoencoders (DAs) are variants of diffusion generative models that use an input-dependent latent variable to capture representations alongside the diffusion process. These representations, to varying extents, can be used for…

Machine Learning · Computer Science 2025-06-03 Magdalena Proszewska , Nikolay Malkin , N. Siddharth