相关论文: On False Accuracy Verification of UMUSCL Scheme

In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…

We present a new numerical scheme which combines the Spectral Difference (SD) method up to arbitrary high order with \emph{a-posteriori} limiting using the classical MUSCL-Hancock scheme as fallback scheme. It delivers very accurate…

Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational fluid dynamics for design problems. An…

We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…

Gauge non-invariance due to material truncation has recently been explored in a number of contexts in strong-coupling QED. We show that the approach proposed recently in Nature Physics 15, 803 (2019) rests on an incorrect mathematical…

Uncertainty estimation (UE) aims to detect hallucinated outputs of large language models (LLMs) to improve their reliability. However, UE metrics often exhibit unstable performance across configurations, which significantly limits their…

We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…

This work proposes and analyzes a fully discrete numerical scheme for solving the Landau-Lifshitz-Gilbert (LLG) equation, which achieves fourth-order spatial accuracy and third-order temporal accuracy.Spatially, fourth-order accuracy is…

A key issue in making precise predictions in perturbative QCD is the uncertainty in setting the renormalization scale. If in principle, the entire perturbative series is void of this issue, in practice the perturbative corrections are known…

Clustering algorithms rely on complex optimisation processes that may be difficult to comprehend, especially for individuals who lack technical expertise. While many explainable artificial intelligence techniques exist for supervised…

Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large…

An overset grid method was used to investigate the interaction between a particle-laden flow and a circular cylinder. The overset grid method was implemented in the Pencil Code , a high-order finite-difference code for compressible flow…

In any calculation in perturbative Quantum Chromodynamics (QCD) a choice needs to be made for the unphysical renormalisation scale, $\mu_R$. The Brodsky-Lepage-Mackenzie/Principle of Maximum Conformality (BLM/PMC) scale-setting procedure is…

Given any algorithm for convex optimization that uses exact first-order information (i.e., function values and subgradients), we show how to use such an algorithm to solve the problem with access to inexact first-order information. This is…

We develop a nonclassicality criterion for the interference of three delayed, but otherwise identical, light fields in a three-mode Bell interferometer. We do so by comparing the prediction of quantum mechanics with those of a classical…

Energy functionals produced by second-order homogenization of periodic elastic structures commonly feature negative gradient moduli. We show that this undesirable property is caused by the truncation of the energy expansion in powers of the…

Classical learning theory describes a well-characterised U-shaped relationship between model complexity and prediction error, reflecting a transition from underfitting in underparameterised regimes to overfitting as complexity grows. Recent…

In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…

In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$…

Class imbalance in real-world data poses a common bottleneck for machine learning tasks, since achieving good generalization on under-represented examples is often challenging. Mitigation strategies, such as under or oversampling the data…