Related papers: A remark on Domain Decomposition approaches solvin…

The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing the required solutions to algebraic Riccati equations.…

Recent works on domain adaptation reveal the effectiveness of adversarial learning on filling the discrepancy between source and target domains. However, two common limitations exist in current adversarial-learning-based methods. First,…

Multi-source domain adaptation (DA) aims at leveraging information from more than one source domain to make predictions in a target domain, where different domains may have different data distributions. Most existing methods for…

Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…

In this paper, we propose a novel overlapping domain decomposition method that can be applied to various problems in variational imaging such as total variation minimization. Most of recent domain decomposition methods for total variation…

In the absence of sufficient data variation (e.g., scanner and protocol variability) in annotated data, deep neural networks (DNNs) tend to overfit during training. As a result, their performance is significantly lower on data from unseen…

We propose a certified reduced basis approach for the strong- and weak-constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model. While the standard strong-constraint 4D-Var approach uses the…

The four-dimensional variational data assimilation (4D-Var) has emerged as an important methodology, widely used in numerical weather prediction, oceanographic modeling, and climate forecasting. Classical unconstrained gradient-based…

Shape-morphing solutions (also known as evolutional deep neural networks, reduced-order nonlinear solutions, and neural Galerkin schemes) are a new class of methods for approximating the solution of time-dependent partial differential…

Domain adaptation (DA) is a technique that transfers predictive models trained on a labeled source domain to an unlabeled target domain, with the core difficulty of resolving distributional shift between domains. Currently, most popular DA…

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

Unsupervised domain adaptation (UDA) in 3D segmentation tasks presents a formidable challenge, primarily stemming from the sparse and unordered nature of point cloud data. Especially for LiDAR point clouds, the domain discrepancy becomes…

The success of supervised classification of remotely sensed images acquired over large geographical areas or at short time intervals strongly depends on the representativity of the samples used to train the classification algorithm and to…

This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of…

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…

Typically a classifier trained on a given dataset (source domain) does not performs well if it is tested on data acquired in a different setting (target domain). This is the problem that domain adaptation (DA) tries to overcome and, while…

In variational assimilation, the most probable state of a dynamical system under Gaussian assumptions for the prior and likelihood can be found by solving a least-squares minimization problem . In recent years, we have seen the popularity…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…

This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of…