20.500.12556/RUL-168092 Probabilistic grammars for modeling dynamical systems from coarse, noisy, and partial data 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. ordinary differential equations equation discovery mathematical modeling system identification symbolic regression partial observability probabilistic context-free grammars odkrivanje enačb diferencialne enačbe strojno učenje true false true Angleški jezik Slovenski jezik Članek v reviji 2025-03-28 12:50:25 2025-03-28 12:50:28 2025-03-29 04:14:36 0000-00-00 00:00:00 2024 0 0 Str. 7689-7721 iss. 10 Vol. 113 Oct. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 004.8 1573-0565 10.1007/s10994-024-06522-1 230493443 s10994-024-06522-1_(1).pdf s10994-024-06522-1_(1).pdf 1 8AA63032E011C9B51C2696BB05EEF0A9 5b443a85885e9ba5778a203ba80026e61bcda99fb025b7a729e3f3c02a77a3d7 1addecdf-0bca-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=201099 https://link.springer.com/article/10.1007/s10994-024-06522-1 1 d08b8245-0bc9-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=201098 Fakulteta za matematiko in fiziko 0 0 0