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

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

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.

• Jezik: Angleški jezik
• Ključne besede: ordinary differential equations, equation discovery, mathematical modeling, system identification, symbolic regression, partial observability, probabilistic context-free grammars
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2024
• Št. strani: Str. 7689-7721
• Številčenje: Vol. 113, iss. 10
• PID: 20.500.12556/RUL-168092
• UDK: 004.8
• ISSN pri članku: 1573-0565
• DOI: 10.1007/s10994-024-06522-1
• COBISS.SI-ID: 230493443
• Datum objave v RUL: 28.03.2025

Gradivo je del revije

• Naslov: Machine learning
• Skrajšan naslov: Mach. learn.
• Založnik: Springer Nature
• ISSN: 1573-0565
• COBISS.SI-ID: 513211417

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: odkrivanje enačb, diferencialne enačbe, strojno učenje