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2020-07-28Zeitschriftenartikel DOI: 10.18452/22317
Reconstructing complex system dynamics from time series: a method comparison
dc.contributor.authorHassanibesheli, Forough
dc.contributor.authorBoers, Niklas
dc.contributor.authorKurths, Jürgen
dc.date.accessioned2021-01-08T09:13:00Z
dc.date.available2021-01-08T09:13:00Z
dc.date.issued2020-07-28none
dc.identifier.other10.1088/1367-2630/ab9ce5
dc.identifier.urihttp://edoc.hu-berlin.de/18452/22948
dc.description.abstractModeling complex systems with large numbers of degrees of freedom has become a grand challenge over the past decades. In many situations, only a few variables are actually observed in terms of measured time series, while the majority of variables—which potentially interact with the observed ones—remain hidden. A typical approach is then to focus on the comparably few observed, macroscopic variables, assuming that they determine the key dynamics of the system, while the remaining ones are represented by noise. This naturally leads to an approximate, inverse modeling of such systems in terms of stochastic differential equations (SDEs), with great potential for applications from biology to finance and Earth system dynamics. A well-known approach to retrieve such SDEs from small sets of observed time series is to reconstruct the drift and diffusion terms of a Langevin equation from the data-derived Kramers–Moyal (KM) coefficients. For systems where interactions between the observed and the unobserved variables are crucial, the Mori–Zwanzig formalism (MZ) allows to derive generalized Langevin equations that contain non-Markovian terms representing these interactions. In a similar spirit, the empirical model reduction (EMR) approach has more recently been introduced. In this work we attempt to reconstruct the dynamical equations of motion of both synthetical and real-world processes, by comparing these three approaches in terms of their capability to reconstruct the dynamics and statistics of the underlying systems. Through rigorous investigation of several synthetical and real-world systems, we confirm that the performance of the three methods strongly depends on the intrinsic dynamics of the system at hand. For instance, statistical properties of systems exhibiting weak history-dependence but strong state-dependence of the noise forcing, can be approximated better by the KM method than by the MZ and EMR approaches. In such situations, the KM method is of a considerable advantage since it can directly approximate the state-dependent noise. However, limitations of the KM approximation arise in cases where non-Markovian effects are crucial in the dynamics of the system. In these situations, our numerical results indicate that methods that take into account interactions between observed and unobserved variables in terms of non-Markovian closure terms (i.e., the MZ and EMR approaches), perform comparatively better.eng
dc.language.isoengnone
dc.publisherHumboldt-Universität zu Berlin
dc.rights(CC BY 4.0) Attribution 4.0 Internationalger
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectcomplex systemseng
dc.subjectstochastic time serieseng
dc.subjectLangevin equationeng
dc.subjectgeneralized Langevin equationeng
dc.subjectdata-driven stochastic differential equation modelseng
dc.subject.ddc530 Physiknone
dc.titleReconstructing complex system dynamics from time series: a method comparisonnone
dc.typearticle
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/22948-6
dc.identifier.doihttp://dx.doi.org/10.18452/22317
dc.type.versionpublishedVersionnone
local.edoc.container-titleNew journal of physicsnone
local.edoc.pages23none
local.edoc.anmerkungThis article was supported by the German Research Foundation (DFG) and the Open Access Publication Fund of Humboldt-Universität zu Berlin.none
local.edoc.type-nameZeitschriftenartikel
local.edoc.institutionMathematisch-Naturwissenschaftliche Fakultätnone
local.edoc.container-typeperiodical
local.edoc.container-type-nameZeitschrift
local.edoc.container-publisher-nameDt. Physikalische Ges. , IOPnone
local.edoc.container-publisher-place[Bad Honnef] , [London]none
local.edoc.container-volume22none
dc.description.versionPeer Reviewednone
local.edoc.container-articlenumber073053none
dc.identifier.eissn1367-2630

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