Related papers: Adaptive Artificial Anti-Diffusion Methods for Hyp…
In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative…
For computational acoustics, schemes need to have low-dispersion and low-dissipation properties in order to capture the amplitude and phase of the wave correctly. To improve the spectral properties of the scheme, the authors have previously…
The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
Unsupervised Anomaly Detection (UAD) methods aim to identify anomalies in test samples comparing them with a normative distribution learned from a dataset known to be anomaly-free. Approaches based on generative models offer…
Alternative finite difference Weighted Essentially Non-Oscillatory (AFD-WENO) schemes allow us to very efficiently update hyperbolic systems even in complex geometries. Recent innovations in AFD-WENO methods allow us to treat hyperbolic…
Diffusion policies have recently emerged as a powerful class of visuomotor controllers for robot manipulation, offering stable training and expressive multi-modal action modeling. However, existing approaches typically treat action…
We introduce new adaptive schemes for the one- and two-dimensional hyperbolic systems of conservation laws. Our schemes are based on an adaption strategy recently introduced in [{\sc S. Chu, A. Kurganov, and I. Menshov}, Appl. Numer. Math.,…
This paper introduces the method of anisotropic diffusion oscillation reduction (ADOR) for shock wave computations. The connection is made between digital image processing,in particular, image edge detection, and numerical shock capturing.…
The active flux (AF) method is a compact high-order finite volume method that evolves cell averages and point values at cell interfaces independently. Within the method of lines framework, the point value can be updated based on Jacobian…
Diffusion models have shown superior performance on unsupervised anomaly detection tasks. Since trained with normal data only, diffusion models tend to reconstruct normal counterparts of test images with certain noises added. However, these…
Several competing artificial compressibility methods for the incompressible flow equations are examined using the high-order flux reconstruction method. The established artificial compressibility method (ACM) of \citet{Chorin1967} is…
Imperceptible adversarial attacks aim to fool DNNs by adding imperceptible perturbation to the input data. Previous methods typically improve the imperceptibility of attacks by integrating common attack paradigms with specifically designed…
Recently anomaly detection (AD) has become an important application for target detection in hyperspectral remotely sensed images. In many applications, in addition to high accuracy of detection we need a fast and reliable algorithm as well.…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
A defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous two-time levels. In the defect…
Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of…
Traditional reconstruction-based methods have struggled to achieve competitive performance in anomaly detection. In this paper, we introduce Denoising Diffusion Anomaly Detection (DDAD), a novel denoising process for image reconstruction…
In this work, we study two-dimensional diffusion-wave equations with variable exponent, modeling mechanical diffusive wave propagation in viscoelastic media with spatially varying properties. We first transform the diffusion-wave model into…
Anomaly detection (AD) plays a vital role across a wide range of real-world domains by identifying data instances that deviate from expected patterns, potentially signaling critical events such as system failures, fraudulent activities, or…