Related papers: An $hp$-adaptive multi-element stochastic collocat…

Human pose estimation has been widely studied with much focus on supervised learning requiring sufficient annotations. However, in real applications, a pretrained pose estimation model usually need be adapted to a novel domain with no…

We consider the standard adaptive finite element loop SOLVE, ESTIMATE, MARK, REFINE, with ESTIMATE being implemented using the $p$-robust equilibrated flux estimator, and MARK being D\"orfler marking. As a refinement strategy we employ…

The paper concerns the problem of pointwise adaptive estimation in regression when the noise is heteroscedastic and incorrectly known. The use of the local approximation method, which includes the local polynomial smoothing as a particular…

Transmission expansion planning (TEP) plays a critical role in ensuring power system reliability and facilitating the integration of renewable energy resources. However, this process requires planners to constantly deal with significant…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

Positional encodings are a common component of neural scene reconstruction methods, and provide a way to bias the learning of neural fields towards coarser or finer representations. Current neural surface reconstruction methods use a…

Optimizing the reliability and the robustness of a design is important but often unaffordable due to high sample requirements. Surrogate models based on statistical and machine learning methods are used to increase the sample efficiency.…

Scene Text Recognition (STR) is challenging in extracting effective character representations from visual data when text is unreadable. Permutation language modeling (PLM) is introduced to refine character predictions by jointly capturing…

In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…

We propose an efficient surrogate modeling technique for uncertainty quantification. The method is based on a well-known dimension-adaptive collocation scheme. We improve the scheme by enhancing sparse polynomial surrogates with conformal…

The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…

Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations,…

We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…

Multigrid methods are popular for solving linear systems derived from discretizing PDEs. Local Fourier Analysis (LFA) is a technique for investigating and tuning multigrid methods. P-multigrid is popular for high-order or spectral finite…

State-of-the-art learned reconstruction methods often rely on black-box modules that, despite their strong performance, raise questions about their interpretability and robustness. Here, we build on a recently proposed image reconstruction…

This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology…

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on…

We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…

This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…

Spatio-temporal forecasting is essential for understanding future dynamics within real-world systems by leveraging historical data from multiple locations. Existing methods often prioritize the development of intricate neural networks to…