The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring effective equations from data is discussed; this protocol allows to check the validity of our results. In addition we show that, with a suitable treatment of time series, such protocol can be used to infer effective models from experimental data. We briefly discuss the practical and conceptual difficulties of a pure data-driven approach in the building of models.

Effective equations in complex systems: From Langevin to machine learning / Vulpiani, A.; Baldovin, M.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2020:1(2020), p. 014003. [10.1088/1742-5468/ab535c]

Effective equations in complex systems: From Langevin to machine learning

Vulpiani A.
;
Baldovin M.
2020

Abstract

The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring effective equations from data is discussed; this protocol allows to check the validity of our results. In addition we show that, with a suitable treatment of time series, such protocol can be used to infer effective models from experimental data. We briefly discuss the practical and conceptual difficulties of a pure data-driven approach in the building of models.
2020
coarse-graining; dynamical processes; stochastic processes
01 Pubblicazione su rivista::01a Articolo in rivista
Effective equations in complex systems: From Langevin to machine learning / Vulpiani, A.; Baldovin, M.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2020:1(2020), p. 014003. [10.1088/1742-5468/ab535c]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1407661
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