Related papers: Topological Approach for Data Assimilation

We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted…

Fitting nonlinear dynamical models to sparse and noisy observations is fundamentally challenging. Identifying dynamics requires data assimilation (DA) to estimate system states, but DA requires an accurate dynamical model. To break this…

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…

Seismic data denoising is an important part of seismic data processing, which directly relate to the follow-up processing of seismic data. In terms of this issue, many authors proposed many methods based on rank reduction, sparse…

The ultra-long relaxation time of glass transition makes it difficult to construct atomic models of amorphous materials by conventional methods. We propose a novel method for building such atomic models using data assimilation method by…

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…

When the heat released by a flame is sufficiently in phase with the acoustic pressure, a self-excited thermoacoustic oscillation can arise. These nonlinear oscillations are one of the biggest challenges faced in the design of safe and…

Data assimilation (DA) is a cornerstone of scientific and engineering applications, combining model forecasts with sparse and noisy observations to estimate latent system states. Classical high-dimensional DA methods, such as the ensemble…

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 a cornerstone of atmospheric system modeling, tasked with reconstructing system states by integrating sparse, noisy observations with prior estimation. While traditional approaches like variational and ensemble Kalman…

Ensemble data assimilation techniques form an indispensable part of numerical weather prediction. As the ensemble size grows and model resolution increases, the amount of required storage becomes a major issue. Data compression schemes may…

One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…

Topological loss based on persistent homology has shown promise in various applications. A topological loss enforces the model to achieve certain desired topological property. Despite its empirical success, less is known about the…

In recent years, machine learning (ML) has been proposed to devise data-driven parametrisations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense,…

A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…

Data assimilation provides a systematic framework for combining dynamical models with partial and noisy observations to infer the evolving state of a system. In this work, we undertake a comparative study of Data Assimilation with Transfer…

Data assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modelling is an important element in data assimilation algorithms which…

In recent years, topological data analysis has been utilized for a wide range of problems to deal with high dimensional noisy data. While text representations are often high dimensional and noisy, there are only a few work on the…

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…