Probabilistic grammars for modeling dynamical systems from coarse, noisy, and partial data

Omejc, Nina (author), Gec, Boštjan (author), Brence, Jure (author), Todorovski, Ljupčo (author), Džeroski, Sašo (author)

Ordinary differential equations (ODEs) are a widely used formalism for the mathematical modeling of dynamical systems, a task omnipresent in scientific domains. The paper introduces a novel method for inferring ODEs from data, which extends ProGED, a method for equation discovery that allows users to formalize domain-specific knowledge as probabilistic context-free grammars and use it for constraining the space of candidate equations. The extended method can discover ODEs from partial observations of dynamical systems, where only a subset of state variables can be observed. To evaluate the performance of the newly proposed method, we perform a systematic empirical comparison with alternative state-of-the-art methods for equation discovery and system identification from complete and partial observations. The comparison uses Dynobench, a set of ten dynamical systems that extends the standard Strogatz benchmark. We compare the ability of the considered methods to reconstruct the known ODEs from synthetic data simulated at different temporal resolutions. We also consider data with different levels of noise, i.e., signal-to-noise ratios. The improved ProGED compares favourably to state-of-the-art methods for inferring ODEs from data regarding reconstruction abilities and robustness to data coarseness, noise, and completeness.

• Language: English
• Keywords: ordinary differential equations, equation discovery, mathematical modeling, system identification, symbolic regression, partial observability, probabilistic context-free grammars
• 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: 2024
• Number of pages: Str. 7689-7721
• Numbering: Vol. 113, iss. 10
• PID: 20.500.12556/RUL-168092
• UDC: 004.8
• ISSN on article: 1573-0565
• DOI: 10.1007/s10994-024-06522-1
• COBISS.SI-ID: 230493443
• Publication date in RUL: 28.03.2025

Record is a part of a journal

• Title: Machine learning
• Shortened title: Mach. learn.
• Publisher: Springer Nature
• ISSN: 1573-0565
• COBISS.SI-ID: 513211417

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.

Secondary language

• Language: Slovenian
• Keywords: odkrivanje enačb, diferencialne enačbe, strojno učenje