Related papers: Learned Discretization Schemes for the Second-Orde…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of…
The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical…
Unsupervised representation learning has proved to be a critical component of anomaly detection/localization in images. The challenges to learn such a representation are two-fold. Firstly, the sample size is not often large enough to learn…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a…
In many image and signal processing applications, as interferometric synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis or color image restoration in HSV or LCh spaces the data has its range on the one-dimensional…
Interpolation techniques play a central role in Astronomy, where one often needs to smooth irregularly sampled data into a smooth map. In a previous article (Lombardi & Schneider 2001), we have considered a widely used smoothing technique…
Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
The Van Leer approach for the approximation of nonlinear scalar conservation laws is studied in one space dimension. The problem can be reduced to a nonlinear interpolation and we propose a convexity property for the interpolated values. We…
Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space,…
In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by…
In this article, we propose optimal discretization of analog filters (or controllers) based on the theory of sampled-data H-infinity control. We formulate the discretization problem as minimization of the H-infinity norm of the error system…
We study in this paper a multilayer discretization of second order elliptic problems, aimed at providing reliable multilayer discretizations of shallow fluid flow problems with diffusive effects. This discretization is based upon the…
Nonlocal filters are simple and powerful techniques for image denoising. In this paper we study the reformulation of a broad class of nonlocal filters in terms of two functional rearrangements: the decreasing and the relative…
Most recent CNN architectures use average pooling as a final feature encoding step. In the field of fine-grained recognition, however, recent global representations like bilinear pooling offer improved performance. In this paper, we…
A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative…