相关论文: A Generalized Empirical Interpolation Method: appl…

Interpolation and internal painting are one of the basic approaches in image internal painting, which is used to eliminate undesirable parts that occur in digital images or to enhance faulty parts. This study was designed to compare the…

In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator…

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…

This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable…

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 address the problem of reconstructing X-Ray tomographic images from scarce measurements by interpolating missing acquisitions using a self-supervised approach. To do so, we train shallow neural networks to combine two neighbouring…

Finite-sample bias is a pervasive challenge in the estimation of structural equation models (SEMs), especially when sample sizes are small or measurement reliability is low. A range of methods have been proposed to improve finite-sample…

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…

Data reduction procedures are aimed to minimize the impact of data acquisition imperfections on the measurement of data properties with a scientific meaning for the astronomer. To achieve this purpose, appropriate arithmetic manipulations…

The discrete empirical interpolation method (DEIM) is a well-established approach, widely used for state reconstruction using sparse sensor/measurement data, nonlinear model reduction, and interpretable feature selection. We introduce the…

In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems. The method is based on a space-time variational formulation. We provide a residual-based a-posteriori error bound on a space-time level and…

A range of nonlinear image reconstruction procedures based on extremizing the generalized Shannon entropy, Kullback-Leibler cross-entropy and Renyi information measures and proposed by the author in early papers is presented. The…

Conventional approaches of sampling signals follow the celebrated theorem of Nyquist and Shannon. Compressive sampling, introduced by Donoho, Romberg and Tao, is a new paradigm that goes against the conventional methods in data acquisition…

A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…

We consider a family of linear systems $A_\mu \alpha=C$ with system matrix $A_\mu$ depending on a parameter $\mu$ and for simplicity parameter-independent right-hand side $C$. These linear systems typically result from the…

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing…

Finite population inference is a central goal in survey sampling. Probability sampling is the main statistical approach to finite population inference. Challenges arise due to high cost and increasing non-response rates. Data integration…

The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…

A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…

Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…