| Title: | Discovery of exact equations for integer sequences |
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| Authors: | ID Gec, Boštjan, Institut "Jožef Stefan" (Author)
ID Džeroski, Sašo, Institut "Jožef Stefan" (Author)
ID Todorovski, Ljupčo, Institut "Jožef Stefan" (Author) |
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| Files: |  URL - Source URL, visit https://www.mdpi.com/2227-7390/12/23/3745
 PDF - Presentation file, download (425,51 KB)
MD5: 5E0E54021433F833B999C66AA8345911
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IJS - Jožef Stefan Institute
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| Abstract: | Equation discovery, also known as symbolic regression, is the field of machine learning that studies algorithms for discovering quantitative laws, expressed as closed-form equations or formulas, in collections of observed data. The latter is expected to come from measurements of physical systems and, therefore, noisy, moving the focus of equation discovery algorithms towards discovering approximate equations. These loosely match the noisy observed data, rendering them inappropriate for applications in mathematics. In this article, we introduce Diofantos, an algorithm for discovering equations in the ring of integers that exactly match the training data. Diofantos is based on a reformulation of the equation discovery task into the task of solving linear Diophantine equations. We empirically evaluate the performance of Diofantos on reconstructing known equations for more than 27,000 sequences from the online encyclopedia of integer sequences, OEIS. Diofantos successfully reconstructs more than 90% of these equations and clearly outperforms SINDy, a state-of-the-art method for discovering approximate equations, that achieves a reconstruction rate of less than 70%. |
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| Keywords: | symbolic regression, equation discovery, online encyclopedia of integer sequences |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 03.10.2024 |
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| Article acceptance date: | 24.11.2024 |
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| Publication date: | 28.11.2024 |
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| Publisher: | MDPI |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 1-22 |
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| Numbering: | Vol. 12, iss. 23, [article no.] 3745 |
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| Source: | Švica |
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| PID: | 20.500.12556/DiRROS-21780  |
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| UDC: | 004.8 |
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| ISSN on article: | 2227-7390 |
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| DOI: | 10.3390/math12233745 |
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| COBISS.SI-ID: | 230498307 |
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| Copyright: | © 2024 by the authors. |
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| Note: | Nasl. z nasl. zaslona;
Opis vira z dne 27. 3. 2025;
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| Publication date in DiRROS: | 27.03.2025 |
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| Views: | 594 |
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| Downloads: | 372 |
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| Metadata: |    |
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