Related papers: Computational efficiency of fractional diffusion u…
Diffusion models have become a leading paradigm for image super-resolution (SR), but existing methods struggle to guarantee both the high-frequency perceptual quality and the low-frequency structural fidelity of generated images. Although…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
In applied mathematics, especially in optimization, functions are often only provided as so called "Black-Boxes" provided by software packages, or very complex algorithms, which make automatic differentation very complicated or even…
We propose a setup for fractionally cointegrated time series which is formulated in terms of latent integrated and short-memory components. It accommodates nonstationary processes with different fractional orders and cointegration of…
We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special…
As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…
We present an algorithm to efficiently sample first-passage times for fractional Brownian motion. To increase the resolution, an initial coarse lattice is successively refined close to the target, by adding exactly sampled midpoints, where…
In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training…
We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
Estimation and inference in dynamic discrete choice models often relies on approximation to lower the computational burden of dynamic programming. Unfortunately, the use of approximation can impart substantial bias in estimation and results…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
Atomic scale simulations are a key element of modern science in that they allow to understand, and even predict, complex physical or chemical phenomena on the basis of the fundamental laws of nature. Among the different existing atomic…
We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
We propose Fractional Policy Gradients (FPG), a reinforcement learning framework incorporating fractional calculus for long-term temporal modeling in policy optimization. Standard policy gradient approaches face limitations from Markovian…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
We present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…
The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space…