Paper Info
Title
Evolving Generalizable Multigrid-Based Helmholtz Preconditioners with Grammar-Guided Genetic Programming
Abstract
Solving the indefinite Helmholtz equation is not only crucial for the understanding of many physical phenomena but also represents an outstandingly-difficult benchmark problem for the successful application of numerical methods. Here we introduce a new approach for evolving efficient preconditioned iterative solvers for Helmholtz problems with multi-objective grammar-guided genetic programming. Our approach is based on a novel context-free grammar, which enables the construction of multigrid preconditioners that employ a tailored sequence of operations on each discretization level. To find solvers that generalize well over the given domain, we propose a custom method of successive problem difficulty adaption, in which we evaluate a preconditioner's efficiency on increasingly ill-conditioned problem instances. We demonstrate our approach's effectiveness by evolving multigrid-based preconditioners for a two-dimensional indefinite Helmholtz problem that outperform several human-designed methods for different wavenumbers up to systems of linear equations with more than a million unknowns.
Year
DOI
Venue
2022
10.1145/3512290.3528688
PROCEEDINGS OF THE 2022 GENETIC AND EVOLUTIONARY COMPUTATION CONFERENCE (GECCO'22)
Keywords
DocType
Citations 
Genetic Programming, Multigrid, Preconditioning, Helmholtz Equation, Grammar-Based, Shifted Laplacian, Generalization, Multi-Objective, Partial Differential Equations, Artificial Intelligence
Conference
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Jonas Schmitt101.01
Harald Köstler250.74