Related papers: Numerical analysis for subdiffusion problem with n…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…
This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…
Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…
We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of…
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…
Diffusion probabilistic models (DPMs) represent a class of powerful generative models. Despite their success, the inference of DPMs is expensive since it generally needs to iterate over thousands of timesteps. A key problem in the inference…
The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…
We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…
State-of-the-art models for aerosol particle nucleation and growth from a cooling vapor primarily use a nodal method to numerically solve particle growth kinetics. In this method, particles that are smaller than the critical size are…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
In this paper we study elliptic partial differential equations with rapidly varying diffusion coefficient that can be represented as a perturbation of a reference coefficient. We develop a numerical method for efficiently solving multiple…
By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
We extend the frozen density embedding theory to non-integer subsystems' particles numbers. Different features of this formulation are discussed, with special concern for approximate embedding calculations. In particular, we highlight the…
In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet…
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…