Related papers: Adaptive Artificial Anti-Diffusion Methods for Hyp…
Angular dispersion (AD) is a ubiquitous phenomenon in optics after light traverses a diffractive or dispersive device, whereby each wavelength propagates at a different angle. AD is useful in a variety of applications; for example,…
Early detection of anomalies in medical images such as brain MRI is highly relevant for diagnosis and treatment of many conditions. Supervised machine learning methods are limited to a small number of pathologies where there is good…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
Denoising diffusion models have recently achieved remarkable success in image generation, capturing rich information about natural image statistics. This makes them highly promising for image reconstruction, where the goal is to recover a…
Shallow water surface flows commonly entrain sediments, resulting in scouring and/or deposition of the underlying substrate that may strongly influence the pattern of subsequent flow. These coupled phenomena, which can be investigated…
We introduce a new methodology for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities, which we call the $C$-method. We…
Emerging technologies such as Reconfigurable Intelligent Surfaces (RIS) make it possible to optimize some parameters of wireless channels. Conventional approaches require relating the channel and its programmable parameters via a simple…
Stable Diffusion (SD) often produces degraded outputs when the training dataset contains adversarial noise. Adversarial purification offers a promising solution by removing adversarial noise from contaminated data. However, existing…
We introduce a new scheme adaption strategy for one- and two-dimensional hyperbolic systems of conservation laws. The proposed approach builds upon the adaptive framework introduced in [S. Chu, A. Kurganov, and I. Menshov, Appl. Numer.…
We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws are extremely popular because, for multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume…
The effects induced by numerical schemes and mesh geometry on the solution of two-dimensional supersonic inviscid flows are investigated in the context of the compressible Euler equations. Five different finite-difference schemes are…
The Active Flux method is a finite volume method for hyperbolic conservation laws that uses both cell averages and point values as degrees of freedom. Several versions of such methods are currently under development. We focus on third order…
We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…
Subsampling is commonly used to mitigate costs associated with data acquisition, such as time or energy requirements, motivating the development of algorithms for estimating the fully-sampled signal of interest $x$ from partially observed…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
The temperature of the gas in molecular clouds is a key determinant of the characteristic mass of star formation. Ambipolar diffusion (AD) is considered one of the most important heating mechanisms in weakly ionized molecular clouds. In…
Underwater images are severely degraded by wavelength-dependent light absorption and scattering, resulting in color distortion, low contrast, and loss of fine details that hinder vision-based underwater applications. To address these…
Controllability is a fundamental requirement in video synthesis, where accurate alignment with conditioning signals is essential. Existing classifier-free guidance methods typically achieve conditioning indirectly by modeling the joint…
This paper presents a novel approach for denoising Electron Backscatter Diffraction (EBSD) patterns using diffusion models. We propose a two-stage training process with a UNet-based architecture, incorporating an auxiliary regression head…