Automating the Design of Multigrid Methods with Evolutionary Program Synthesis
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 m...
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| Format: | Online |
| Język: | angielski |
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FAU University Press
2025
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| Hasła przedmiotowe: | |
| Dostęp online: | ONIX_20251215T160703_9783961477326_7 |
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| _version_ | 1869520979547389952 |
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| author | Schmitt, Jonas |
| author_browse | Schmitt, Jonas |
| author_facet | Schmitt, Jonas |
| author_sort | Schmitt, Jonas |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-170180 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | FAU University Press |
| publisherStr | FAU University Press |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1701802025-12-16T05:10:48Z Automating the Design of Multigrid Methods with Evolutionary Program Synthesis Schmitt, Jonas formal grammar Künstliche Intelligenz artificial intelligence Computersimulation computer simulation automated algorithm design Programmsynthese multigrid Mehrgitterverfahren Genetische Programmierung program synthesis Formale Grammatik genetic programming 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::UYA Mathematical theory of computation thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence 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. 2025-12-16T05:10:47Z 2025-12-16T05:10:47Z 2025-12-15T15:08:53Z 2024 book ONIX_20251215T160703_9783961477326_7 https://library.oapen.org/handle/20.500.12657/109176 9783961477326 9783961477319 https://directory.doabooks.org/handle/20.500.12854/170180 eng FAU Studien aus der Informatik open access image/jpeg Attribution 4.0 International https://library.oapen.org/bitstream/20.500.12657/109176/1/9783961477326.pdf FAU University Press 10.25593/978-3-96147-732-6 10.25593/978-3-96147-732-6 2c600dea-eece-4066-87be-da335e323fdb 9783961477326 9783961477319 222 Erlangen open access |
| spellingShingle | formal grammar Künstliche Intelligenz artificial intelligence Computersimulation computer simulation automated algorithm design Programmsynthese multigrid Mehrgitterverfahren Genetische Programmierung program synthesis Formale Grammatik genetic programming 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::UYA Mathematical theory of computation thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence Schmitt, Jonas Automating the Design of Multigrid Methods with Evolutionary Program Synthesis |
| title | Automating the Design of Multigrid Methods with Evolutionary Program Synthesis |
| title_full | Automating the Design of Multigrid Methods with Evolutionary Program Synthesis |
| title_fullStr | Automating the Design of Multigrid Methods with Evolutionary Program Synthesis |
| title_full_unstemmed | Automating the Design of Multigrid Methods with Evolutionary Program Synthesis |
| title_short | Automating the Design of Multigrid Methods with Evolutionary Program Synthesis |
| title_sort | automating the design of multigrid methods with evolutionary program synthesis |
| topic | formal grammar Künstliche Intelligenz artificial intelligence Computersimulation computer simulation automated algorithm design Programmsynthese multigrid Mehrgitterverfahren Genetische Programmierung program synthesis Formale Grammatik genetic programming 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::UYA Mathematical theory of computation thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence |
| topic_facet | formal grammar Künstliche Intelligenz artificial intelligence Computersimulation computer simulation automated algorithm design Programmsynthese multigrid Mehrgitterverfahren Genetische Programmierung program synthesis Formale Grammatik genetic programming 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::UYA Mathematical theory of computation thema EDItEUR::U Computing and Information Technology::UY Computer science::UYQ Artificial intelligence |
| url | ONIX_20251215T160703_9783961477326_7 |
| work_keys_str_mv | AT schmittjonas automatingthedesignofmultigridmethodswithevolutionaryprogramsynthesis |