Related papers: High order recovery of geometric interfaces from c…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Hierarchical renormalization group transformations are related to non-associative algebras. Non-trivial infrared fixed points are shown to be solutions of polynomial equations. At the example of a scalar model in $d(\ge2)$ dimensions some…
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…
Conventional approaches to human mesh recovery predominantly employ a region-based strategy. This involves initially cropping out a human-centered region as a preprocessing step, with subsequent modeling focused on this zoomed-in image.…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The minimizing functional balances the distance function from the point cloud and the mean curvature…
A basic issue in optimization, inverse theory,neural networks, computational chemistry and many other problems is the geometrical characterization of high dimensional functions. In inverse calculations one aims to characterize the set of…
In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the…
Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…
This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
The aim of this paper is to propose a mechanism to efficiently and explicitly model image hierarchies in the global, regional, and local range for image restoration. To achieve that, we start by analyzing two important properties of natural…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
This paper presents a simple and highly accurate method for capturing sharp interfaces moving in divergence-free velocity fields using the high-order Flux Reconstruction approach on unstructured grids. A well-known limitation of high-order…
We consider the problem of optimal recovery of an element $u$ of a Hilbert space $\mathcal{H}$ from $m$ measurements obtained through known linear functionals on $\mathcal{H}$. Problems of this type are well studied \cite{MRW} under an…
Reconstruction-based methods are widely explored in industrial visual anomaly detection. Such methods commonly require the model to well reconstruct the normal patterns but fail in the anomalies, and thus the anomalies can be detected by…