相关论文: Solve the Master Equation by Python-An Introductio…

We present a novel numerical routine (oscode) with a C++ and Python interface for the efficient solution of one-dimensional, second-order, ordinary differential equations with rapidly oscillating solutions. The method is based on a…

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…

As the field of Quantum Computing continues to grow, so too has the general public's interest in testing some of the publicly available quantum computers. However, many might find learning all of the supplementary information that goes into…

We present a parallel implementation of a direct solver for the Poisson's equation on extreme-scale supercomputers with accelerators. We introduce a chunked-pencil decomposition as the domain-decomposition strategy to distribute work among…

Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning…

The present study is meant to fill in some information gaps occurring in the most widespread and well-known educational and reference literature about programming. The stress is laid on a very useful instrument - the bitwise operations,…

This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes.…

Constraint-satisfaction problems (CSPs) are ubiquitous, ranging from budgeting for grocery shopping to verifying software behavior. Logic modeling helps solve CSPs programmatically using SMT solvers. Despite its importance in many Computer…

Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…

Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the…

Algorithmic fairness has received considerable attention due to the failures of various predictive AI systems that have been found to be unfairly biased against subgroups of the population. Many approaches have been proposed to mitigate…

We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is…

Once an optimisation problem has been solved, the solution may need adaptation when contextual factors change. This challenge, also known as reoptimisation, has been addressed in various problem domains, such as railway crew rescheduling,…

For a system of linear partial differential equations (LPDEs) we introduce an operator equation for auxiliary operators. These operators are used to construct a kernel of an integral transformation leading the LPDE to the separation of…

Many nonlinear PDEs have singular or oscillatory solutions or may exhibit physical instabilities or uncertainties. This requires a suitable concept of physically relevant generalized solutions. Dissipative measure-valued solutions have been…

Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on the world's largest computers are spent simulating problems…

This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal…

Piecewise-affine (PWA) systems are widely used for modeling and control of robotics problems including modeling contact dynamics. A common approach is to encode the control problem of the PWA system as a Mixed-Integer Convex Program (MICP),…

Neural Networks (NNs) can be used to solve Ordinary and Partial Differential Equations (ODEs and PDEs) by redefining the question as an optimization problem. The objective function to be optimized is the sum of the squares of the PDE to be…