相关论文: Adaptive refinement in defeaturing problems via an…

This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al.,…

We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error…

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…

Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…

In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…

In asymmetric retrieval systems, models with different capacities are deployed on platforms with different computational and storage resources. Despite the great progress, existing approaches still suffer from a dilemma between retrieval…

In frame-based vision, object detection faces substantial performance degradation under challenging conditions due to the limited sensing capability of conventional cameras. Event cameras output sparse and asynchronous events, providing a…

We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary…

This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…

We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…

Diffusion models have attained remarkable success in the domains of image generation and editing. It is widely recognized that employing larger inversion and denoising steps in diffusion model leads to improved image reconstruction quality.…

We consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e., vector-valued mapped…

We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and…

Prevailing video frame interpolation algorithms, that generate the intermediate frames from consecutive inputs, typically rely on complex model architectures with heavy parameters or large delay, hindering them from diverse real-time…

For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…

For the non-conforming Crouzeix-Raviart boundary elements from [Heuer, Sayas: Crouzeix-Raviart boundary elements, Numer. Math. 112, 2009], we develop and analyze a posteriori error estimators based on the $h-h/2$ methodology. We discuss the…

The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…

We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the…

Adaptive mesh refinement is central to the efficient solution of partial differential equations (PDEs) via the finite element method (FEM). Classical $r$-adaptivity optimizes vertex positions but requires solving expensive auxiliary PDEs…

In this paper a new hp-adaptive strategy for elliptic problems based on refinement history is proposed, which chooses h-, p- or hp-refinement on individual elements according to a posteriori error estimate, as well as smoothness estimate of…