Related papers: GAPS: Generator for Automatic Polynomial Solvers
GMRES is one of the most popular iterative methods for the solution of large linear systems of equations that arise from the discretization of linear well-posed problems, such as Dirichlet boundary value problems for elliptic partial…
Gr\"obner bases are an important tool in computational algebra and, especially in cryptography, often serve as a boilerplate for solving systems of polynomial equations. Research regarding (efficient) algorithms for computing Gr\"obner…
In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the…
The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…
We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a…
Large sparse linear systems of equations are ubiquitous in science and engineering, such as those arising from discretizations of partial differential equations. Algebraic multigrid (AMG) methods are one of the most common methods of…
As intelligent systems and multi-agent coordination become increasingly central to real-world applications, there is a growing need for simulation tools that are both scalable and accessible. Existing high-fidelity simulators, while…
A generalized criterion for signature related algorithms to compute Gr\"obner basis is proposed in this paper. Signature related algorithms are a popular kind of algorithms for computing Gr\"obner basis, including the famous F5 algorithm,…
This article describes haggies, a program for the generation of optimised programs for the efficient numerical evaluation of mathematical expressions. It uses a multivariate Horner-scheme and Common Subexpression Elimination to reduce the…
Many statistical problems involve optimization over a discrete parameter space having an unknown dimension. In such settings, gradient-based methods often fail due to the non-differentiability of the objective function or a non-convex or…
We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes…
We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gr\"obner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation…
Auto-regressive frameworks for next-scale prediction of 2D images have demonstrated strong potential for producing diverse and sophisticated content by progressively refining a coarse input. However, extending this paradigm to 3D object…
With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs…
Generative neural networks are able to mimic intricate probability distributions such as those of handwritten text, natural images, etc. Since their inception several models were proposed. The most successful of these were based on…
We construct an explicit minimal strong Groebner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m>=2. The proof is done in a purely combinatorial way. It is a remarkable fact that the constructed Groebner…
The main goal of the Artap project is to provide an extensive infrastructure for robust design optimization, where usually many different numerical solvers have to be used together and the impact of the manufacturing uncertainties have to…
Generative adversarial networks (GANs) are one of the greatest advances in AI in recent years. With their ability to directly learn the probability distribution of data, and then sample synthetic realistic data. Many applications have…
A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate…
Developing suitable approximate models for analyzing and simulating complex nonlinear systems is practically important. This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian…