20.500.12556/DiRROS-21780 Discovery of exact equations for integer sequences 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%. symbolic regression equation discovery online encyclopedia of integer sequences odkrivanje enačb true false true MDPI Švica Angleški jezik Slovenski jezik © 2024 by the authors. Neznano 2025-03-27 14:52:10 2025-03-27 14:52:10 2025-10-24 03:49:49 0000-00-00 00:00:00 2024 0 0 Nasl. z nasl. zaslona; Opis vira z dne 27. 3. 2025; str. 1-22 iss. 23, [article no.] 3745 Vol. 12 Dec. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2024-10-03 2024-11-24 2024-11-28 004.8 2227-7390 10.3390/math12233745 230498307 https://www.mdpi.com/2227-7390/12/23/3745 1 aee59ab9-0b12-11f0-963a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=31390 RAZ_Gec_Bostjan_2024.pdf RAZ_Gec_Bostjan_2024.pdf 1 5E0E54021433F833B999C66AA8345911 f9abceab45726729c2944319108a427d39b0dda09e60afdf9be0c74355db5314 2c2db945-0b13-11f0-963a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=31391 Institut Jožef Stefan 0 0 0