Symbolic Neural Architecture Search for Differential Equations
In this paper, we introduce the first use of symbolic integration that leverages the machine learning infrastructure, such as automatic differentiation, to find analytical approximations of ordinary and partial differential equations. Analytical solutions to differential equations are at the core of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10354328/ |
| _version_ | 1797376318689509376 |
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| author | Paulius Sasnauskas Linas Petkevicius |
| author_facet | Paulius Sasnauskas Linas Petkevicius |
| author_sort | Paulius Sasnauskas |
| collection | DOAJ |
| description | In this paper, we introduce the first use of symbolic integration that leverages the machine learning infrastructure, such as automatic differentiation, to find analytical approximations of ordinary and partial differential equations. Analytical solutions to differential equations are at the core of fundamental mathematical models, which often cannot be determined analytically because of model complexity or non-linearity. Traditionally, the methods for solving these problems have used hand-designed strategies, numerical methods, or iterative methods. We propose a method that is an application of differentiable architecture search to find solutions to differential equations. We demonstrate our proposed method on a set of equations while simultaneously comparing it with numerical solutions to corresponding problems. We demonstrate that the proposed framework allows for solutions to various problems. |
| first_indexed | 2024-03-08T19:36:49Z |
| format | Article |
| id | doaj.art-e51171aca79044febe885209b6a04e94 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-08T19:36:49Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-e51171aca79044febe885209b6a04e942023-12-26T00:11:13ZengIEEEIEEE Access2169-35362023-01-011114123214124010.1109/ACCESS.2023.334202310354328Symbolic Neural Architecture Search for Differential EquationsPaulius Sasnauskas0https://orcid.org/0000-0002-6379-013XLinas Petkevicius1https://orcid.org/0000-0003-2416-0431Institute of Computer Science, Vilnius University, Vilnius, LithuaniaInstitute of Computer Science, Vilnius University, Vilnius, LithuaniaIn this paper, we introduce the first use of symbolic integration that leverages the machine learning infrastructure, such as automatic differentiation, to find analytical approximations of ordinary and partial differential equations. Analytical solutions to differential equations are at the core of fundamental mathematical models, which often cannot be determined analytically because of model complexity or non-linearity. Traditionally, the methods for solving these problems have used hand-designed strategies, numerical methods, or iterative methods. We propose a method that is an application of differentiable architecture search to find solutions to differential equations. We demonstrate our proposed method on a set of equations while simultaneously comparing it with numerical solutions to corresponding problems. We demonstrate that the proposed framework allows for solutions to various problems.https://ieeexplore.ieee.org/document/10354328/Symbolic integrationmachine learningPDEneural architecture search |
| spellingShingle | Paulius Sasnauskas Linas Petkevicius Symbolic Neural Architecture Search for Differential Equations IEEE Access Symbolic integration machine learning PDE neural architecture search |
| title | Symbolic Neural Architecture Search for Differential Equations |
| title_full | Symbolic Neural Architecture Search for Differential Equations |
| title_fullStr | Symbolic Neural Architecture Search for Differential Equations |
| title_full_unstemmed | Symbolic Neural Architecture Search for Differential Equations |
| title_short | Symbolic Neural Architecture Search for Differential Equations |
| title_sort | symbolic neural architecture search for differential equations |
| topic | Symbolic integration machine learning PDE neural architecture search |
| url | https://ieeexplore.ieee.org/document/10354328/ |
| work_keys_str_mv | AT pauliussasnauskas symbolicneuralarchitecturesearchfordifferentialequations AT linaspetkevicius symbolicneuralarchitecturesearchfordifferentialequations |