Explore
Automating the Design of Multigrid Methods with Evolutionary Program Synthesis
Jonas Schmitt
2024
0 Ungluers have
Faved this Work
Login to Fave
Many of the most fundamental laws of nature can be formulated as partial differential equations (PDEs). However, since the general solution of many PDEs is unknown, the efficient approximate solution of these equations is one of humanity's greatest challenges. While multigrid represents one of the most effective methods for solving PDEs numerically, in many cases, the design of an efficient or at least working multigrid solver is an open problem. This thesis demonstrates that grammar-guided genetic programming, an evolutionary program synthesis technique, can discover multigrid methods of unprecedented structure that achieve a high degree of efficiency and generalization. For this purpose, we develop a novel context-free grammar that enables the automated generation of multigrid methods in a symbolically-manipulable formal language, based on which we can apply the same multigrid-based solver to problems of different sizes without having to adapt its internal structure. Treating the automated design of an efficient multigrid method as a program synthesis task allows us to find novel sequences of multigrid operations, including the combination of different smoothing and coarse-grid correction steps on each level of the discretization hierarchy.
This book is included in DOAB.
Why read this book? Have your say.
You must be logged in to comment.
Rights Information
Are you the author or publisher of this work? If so, you can claim it as yours by registering as an Unglue.it rights holder.Downloads
This work has been downloaded 0 times via unglue.it ebook links.
- 0 - pdf (CC BY) at OAPEN Library.
Keywords
- artificial intelligence
- automated algorithm design
- Computer simulation
- Computersimulation
- formal grammar
- Formale Grammatik
- genetic programming
- Genetische Programmierung
- Künstliche Intelligenz
- Mehrgitterverfahren
- multigrid
- program synthesis
- Programmsynthese
- thema EDItEUR::U Computing and Information Technology::UY Computer science::UYA Mathematical theory of computation
- thema EDItEUR::U Computing and Information Technology::UY Computer science::UYM Computer modelling and simulation
- thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence
Links
DOI: 10.25593/978-3-96147-732-6Editions