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Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…

Numerical Analysis · Mathematics 2011-08-02 Oren E. Livne , Achi Brandt

Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute…

Numerical Analysis · Mathematics 2022-05-31 Victor A. Paludetto Magri , Robert D. Falgout , Ulrike M. Yang

We develop algorithms capable of tackling robust black-box optimisation problems, where the number of model runs is limited. When a desired solution cannot be implemented exactly the aim is to find a robust one, where the worst case in an…

Optimization and Control · Mathematics 2020-04-17 Martin Hughes , Marc Goerigk , Trivikram Dokka

Grammars provide a convenient and powerful mechanism to define the space of possible solutions for a range of problems. However, when used in grammatical evolution (GE), great care must be taken in the design of a grammar to ensure that the…

Neural and Evolutionary Computing · Computer Science 2022-04-18 Grant Dick , Peter A. Whigham

Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a…

Neural and Evolutionary Computing · Computer Science 2017-04-05 Léo Françoso Dal Piccol Sotto , Vinícius Veloso de Melo

The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…

Numerical Analysis · Mathematics 2024-03-14 Francisco Holguin , GS Sidharth , Gavin Portwood

We present a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the iterative solution of the linear systems of equations…

Numerical Analysis · Mathematics 2025-06-18 Paola F. Antonietti , Matteo Caldana , Luca Dede'

Functions of chemical composition are complex and discrete in nature making it impossible to optimize them with gradient methods. Genetic algorithms, which do not use derivative information, are used to maximize the thermal conductivity of…

Materials Science · Physics 2018-01-30 Alexander Kerr , Kieran Mullen

Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing computation for multiprocessor…

Data Structures and Algorithms · Computer Science 2017-09-26 Orlando Moreira , Merten Popp , Christian Schulz

The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…

Mathematical Software · Computer Science 2020-06-19 Charles D. Murray , Tobias Weinzierl

Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with…

Mathematical Software · Computer Science 2020-07-02 Sashikumaar Ganesan , Manan Shah

Learning ensembles by bagging can substantially improve the generalization performance of low-bias, high-variance estimators, including those evolved by Genetic Programming (GP). To be efficient, modern GP algorithms for evolving (bagging)…

Neural and Evolutionary Computing · Computer Science 2021-02-08 Marco Virgolin

The advent of Large Language Models (LLMs) has opened new frontiers in automated algorithm design, giving rise to numerous powerful methods. However, these approaches retain critical limitations: they require extensive evaluation of the…

Neural and Evolutionary Computing · Computer Science 2026-02-05 Haoran Yin , Shuaiqun Pan , Zhao Wei , Jian Cheng Wong , Yew-Soon Ong , Anna V. Kononova , Thomas Bäck , Niki van Stein

Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of…

Mathematical Software · Computer Science 2020-01-22 Wayne B. Mitchell , Robert Strzodka , Robert D. Falgout

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

Numerical Analysis · Mathematics 2025-06-18 Matteo Caldana , Paola F. Antonietti , Luca Dede'

This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…

Numerical Analysis · Mathematics 2013-10-01 Markus Blatt , Olaf Ippisch , Peter Bastian

Recently, more and more 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…

Neural and Evolutionary Computing · Computer Science 2020-04-08 Cheng He , Shihua Huang , Ran Cheng , Kay Chen Tan , Yaochu Jin

Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…

Numerical Analysis · Mathematics 2012-06-11 Oren E. Livne , Achi Brandt

Ensemble learning is a powerful paradigm that has been usedin the top state-of-the-art machine learning methods like Random Forestsand XGBoost. Inspired by the success of such methods, we have devel-oped a new Genetic Programming method…

Neural and Evolutionary Computing · Computer Science 2020-01-22 Nuno M. Rodrigues , João E. Batista , Sara Silva

The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…

Numerical Analysis · Computer Science 2015-03-19 Peter R. Brune , Matthew G. Knepley , L. Ridgway Scott