Related papers: A remark on Domain Decomposition approaches solvin…

A non-intrusive data assimilation methodology is developed to improve the statistical predictions of large-eddy simulations (LES). The ensemble-variational (EnVar) approach aims to minimize a cost function that is defined as the discrepancy…

Continuous data assimilation (CDA) techniques, most notably the nudging approach proposed by Azouani, Olson, and Titi (AOT), have been shown to be very successful in deterministic frameworks for achieving long-time synchronization between…

Data Assimilation is the process in which we improve the representation of the state of a physical system by combining information coming from a numerical model, real-world observations, and some prior modelling. It is widely used to model…

Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…

Sea ice dynamics are crucial to the global climate system, yet traditional continuum (e.g., viscous-plastic) models often fail to represent the discrete floe interactions that dominate in the marginal ice zone. Lagrangian discrete element…

We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our…

Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a…

Deep learning has recently gained attention in the atmospheric and oceanic sciences for its potential to improve the accuracy of numerical simulations or to reduce computational costs. Super-resolution is one such technique for…

Deep Neural Networks (DNNs) have recently been achieving state-of-the-art performance on a variety of computer vision related tasks. However, their computational cost limits their ability to be implemented in embedded systems with…

The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…

Domain adaption (DA) and domain generalization (DG) are two closely related methods which are both concerned with the task of assigning labels to an unlabeled data set. The only dissimilarity between these approaches is that DA can access…

The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…

In this paper, we consider the intersection of two problems in machine learning: Multi-Source Domain Adaptation (MSDA) and Dataset Distillation (DD). On the one hand, the first considers adapting multiple heterogeneous labeled source…

In many practical applications, it is often difficult and expensive to obtain large-scale labeled data to train state-of-the-art deep neural networks. Therefore, transferring the learned knowledge from a separate, labeled source domain to…

Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

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,…

We review an algorithm developed for parameter estimation within the Continuous Data Assimilation (CDA) approach. We present an alternative derivation for the algorithm presented in a paper by Carlson, Hudson, and Larios (CHL, 2021). This…

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…

In many practical applications, it is often difficult and expensive to obtain enough large-scale labeled data to train deep neural networks to their full capability. Therefore, transferring the learned knowledge from a separate, labeled…