Related papers: An accurate, fast, mathematically robust, universa…
To sample from a general target distribution $p_*\propto e^{-f_*}$ beyond the isoperimetric condition, Huang et al. (2023) proposed to perform sampling through reverse diffusion, giving rise to Diffusion-based Monte Carlo (DMC).…
A new lattice Boltzmann model for multicomponent ideal gas mixtures is presented. The model development consists of two parts. First, a new kinetic model for Stefan- Maxwell diffusion amongst the species is proposed and realized as a…
In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation,…
The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to It\^o diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the…
Diffusion coefficients are essential microphysics input for modeling white dwarf evolution, as they impact phase separation at crystallization and sedimentary heat sources. Present schemes for computing diffusion coefficients are accurate…
Audio Super-Resolution is a set of techniques aimed at high-quality estimation of the given signal as if it would be sampled with higher sample rate. Among suggested methods there are diffusion and flow models (which are considered slower),…
The subdiffusion model that involves a Caputo fractional derivative in time is widely used to describe anomalously slow diffusion processes. In this work we aim at recovering the locations of small conductivity inclusions in the model from…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
In this study, we presented the high-order fundamental solutions and general solutions of convection-diffusion equation. To demonstrate their efficacy, we applied the high-order general solutions to the boundary particle method (BPM) for…
Modeling via fractional partial differential equations or a L\'evy process has been an active area of research and has many applications. However, the lack of efficient numerical computation methods for general nonlocal operators impedes…
Diffusion-based image compression methods have achieved notable progress, delivering high perceptual quality at low bitrates. However, their practical deployment is hindered by significant inference latency and heavy computational overhead,…
The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…
Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…