Dimensionally-consistent equation discovery through probabilistic attribute grammars

Brence, Jure (author), Džeroski, Sašo (author), Todorovski, Ljupčo (author)

Equation discovery, also known as symbolic regression, is a machine learning task of inducing closed-form equations from data and background knowledge. The latter takes various forms. Domain-specific knowledge can constrain the space of candidate equations to those that make sense in the scientific or engineering domain of use. Cross-domain knowledge, on the other hand, imposes general rules for model acceptability, such as parsimony, understandability, or consistency of the equations with the dimensional units of the variables. In this paper, we propose using attribute grammars to ensure the induced equations' dimensional consistency. Attribute grammars are flexible enough to combine cross-domain knowledge on dimensional consistency with domain-specific knowledge expressed as a probabilistic context-free grammar. At the same time, we show that attribute grammars can be efficiently transformed into probabilistic context-free grammars for equation discovery with existing algorithms. Finally, we provide empirical evidence that attribute grammars ensuring dimensional consistency of equations can significantly improve the performance of equation discovery on the standard set of a hundred Feynman benchmarks.

• Language: English
• Keywords: equation discovery, symbolic regression, dimensional analysis, units of measurement, background knowledge, background information, computational scientific discovery
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 742-756
• Numbering: Vol. 632
• PID: 20.500.12556/RUL-148320-915b6af9-8f94-252b-de38-5ea24ece57b2
• UDC: 004
• ISSN on article: 1872-6291
• DOI: 10.1016/j.ins.2023.03.073
• COBISS.SI-ID: 151276803
• Publication date in RUL: 11.08.2023

Record is a part of a journal

• Title: Information sciences
• Publisher: Elsevier
• ISSN: 1872-6291
• COBISS.SI-ID: 23178245

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0103
• Name: Tehnologije znanja

• Funder: ARRS - Slovenian Research Agency
• Project number: N2-0128
• Name: Avtomatizirana sinteza in analiza znanstvenih modelov