Related papers: Automated Grammar-based Algebraic Multigrid Design…

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, it is relatively insufficient to empower the…

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…

Large language models (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring…

Among the evolutionary methods, one that is quite prominent is Genetic Programming, and, in recent years, a variant called Geometric Semantic Genetic Programming (GSGP) has shown to be successfully applicable to many real-world problems.…

This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…

In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and…

We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear-quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric…

There are a variety of choices to be made in both computer algebra systems (CASs) and satisfiability modulo theory (SMT) solvers which can impact performance without affecting mathematical correctness. Such choices are candidates for…

We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…

Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…

Algebraic multigrid (AMG) methods derive their optimal efficiency from the interplay between a relaxation process and a corresponding coarse grid correction. In many standard formulations, relaxation and coarse-graining are analyzed and…

Optimization can be found in many real-life applications. Designing an effective algorithm for a specific optimization problem typically requires a tedious amount of effort from human experts with domain knowledge and algorithm design…

This paper presents FLGC, a simple yet effective fully linear graph convolutional network for semi-supervised and unsupervised learning. Instead of using gradient descent, we train FLGC based on computing a global optimal closed-form…

Recently, increasing works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted…

The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…

Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…

In order to find hyperparameters for a machine learning model, algorithms such as grid search or random search are used over the space of possible values of the models hyperparameters. These search algorithms opt the solution that minimizes…

We present superconducting quantum circuits which exhibit atomic energy spectrum and selection rules as ladder and lambda three-level configurations designed by means of genetic algorithms. These heuristic optimization techniques are…

Data-efficient image classification is a challenging task that aims to solve image classification using small training data. Neural network-based deep learning methods are effective for image classification, but they typically require…

For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the…