# Evolving Algebraic Multigrid Methods Using Grammar-Guided Genetic Programming

arXiv: https://arxiv.org/abs/2412.05852 · HTML: https://mlsanity.com/paper/2412.05852/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 8 Dec 2024.

## Builds on (most cited first, 1 of 1)

- [Optimization-Based Algebraic Multigrid Coarsening Using Reinforcement Learning](https://mlsanity.com/paper/2106.01854/) (2021)

## Built on by (most cited first, 2 of 2)

- [Towards Automated Algebraic Multigrid Preconditioner Design Using Genetic Programming for Large-Scale Laser Beam Welding Simulations](https://mlsanity.com/paper/2412.08186/) (2024)
- [An overview of machine learning-enhanced iterative methods for systems of linear and nonlinear equations](https://mlsanity.com/paper/2610.07211/) (2026)

## Abstract (arXiv)

Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and W-cycles. We use grammar rules to generate arbitrary-shaped cycles, wherein the smoothers and their relaxation weights are chosen independently at each step within the cycle. We call this a flexible multigrid cycle. These flexible cycles are used in Algebraic Multigrid (AMG) methods with the help of grammar rules and optimized using genetic programming. The flexible AMG methods are implemented in the software library of hypre, and the programs are optimized separately for two cases: a standalone AMG solver for a 3D anisotropic problem and an AMG preconditioner with conjugate gradient for a multiphysics code. We observe that the optimized flexible cycles provide higher efficiency and better performance than the standard cycle types.