Related papers: A network partition method for solving large-scale…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
The filtering equations govern the evolution of the conditional distribution of a signal process given partial, and possibly noisy, observations arriving sequentially in time. Their numerical approximation plays a central role in many…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the $H^{-1}$-gradient flow of the…
In this paper, we present a machine learning-based data generator framework tailored to aid researchers who utilize simulations to examine various physical systems or processes. High computational costs and the resulting limited data often…
Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level…
Computational methods for discovering patterns of local correlations in sequences are important in computational biology. Here we show how to determine the optimal partitioning of aligned sequences into non-overlapping segments such that…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…
For convolutional neural networks (CNNs) that have a large volume of input data, memory management becomes a major concern. Memory cost reduction can be an effective way to deal with these problems that can be realized through different…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…
Due to the increasing complexity and interconnectedness of different components in modern automotive software systems there is a great number of interactions between these system components and their environment. These interactions result…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…