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In this paper, we develop a robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion equations (tFDEs), superiorly handling the cases of small or vanishing lower bound of the VO function. The valid fast…
In the continuous time random walk model, the time-fractional operator usually expresses an infinite waiting time probability density. Different from that usual setting, this work considers the tempered time-fractional operator, which…
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and…
For $0<\nu_2<\nu_1\leq 1$, we analyze a linear integro-differential equation on the space-time cylinder $\Omega\times(0,T)$ in the unknown $u=u(x,t)$ $$\mathbf{D}_{t}^{\nu_1}(\varrho_{1}u)-\mathbf{D}_{t}^{\nu_2}(\varrho_2…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
We improve the time decay estimates of solutions to the one-dimensional fractional diffusion equation involving the Caputo derivative. The equation is considered on the half-line. Depending on the boundary condition, we show that solutions…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
We derive and prove the `fast response' formula for the linear response, the parameter derivatives of long-time-averaged statistics, of hyperbolic deterministic chaotic systems. The expression is pointwisely defined so we can compute the…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
The aim of this paper is to develop fast second-order accurate difference schemes for solving one- and two-dimensional time distributed-order and Riesz space fractional diffusion equations. We adopt the same measures for one- and…
In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpretations of the numerical schemes which lead to a posteriori…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
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…
We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…
In this paper, we develop fast algorithms for two stochastic submodular maximization problems. We start with the well-studied adaptive submodular maximization problem subject to a cardinality constraint. We develop the first linear-time…
In this paper, we propose a novel machine learning method based on adaptive tensor neural network subspace to solve linear time-fractional diffusion-wave equations and nonlinear time-fractional partial integro-differential equations. In…
Diffusion models have become a leading method for generative modeling of both image and scientific data. As these models are costly to train and \emph{evaluate}, reducing the inference cost for diffusion models remains a major goal.…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…