Data-driven non-Markovian closure models

Kondrashov, Dmitri; Chekroun, Mickaël D.; Ghil, Michael

doi:10.1016/j.physd.2014.12.005

Cited by 121 publications

(182 citation statements)

References 133 publications

Supporting

Mentioning

178

Contrasting

Order By: Relevance

“…The term η(t) accounts for the stochastic forcing that is now uncorrelated with x, as guaranteed by the MZ formalism. The noise term, however, is not necessarily white in time or space; see Kondrashov et al (2015) for a detailed derivation of the GLE approach and Appendix A for a sketch of the main ideas and more technical details. The temporal evolution of both the δ 18 O and dust time series indicates that there exist two alternative, relatively steady states for the underlying dynamical system, namely the colder stadials and the warmer interstadials (Dansgaard et al, 1993;Rasmussen et al, 2014).…”

Section: G(t S; X(s))ds + η(T)mentioning

confidence: 99%

“…It has recently been shown in general terms how to approximate the GLE (2) by a set of SDEs that is relatively easy to derive from the observables x (Kondrashov et al, 2015). Their MSMs both generalize EMR models and provide the correct time-continuous limit of such models.…”

Section: Approximating the Gle In Practicementioning

confidence: 99%

“…Given that the stochastic difference equation (Eq. 4) only approximates the theoretical GLE provided by the MZ formalism, one also needs to validate empirically that the residuals are uncorrelated with the observations x (Kondrashov et al, 2015).…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…The striking success of this empiricalmodel reduction (EMR) approach in reproducing dynamical and statistical properties of the underlying dynamical systems has been explained by embedding EMR models in the larger class of multilayer stochastic models (MSMs); the latter models, in turn, were shown to be solidly grounded in the Mori-Zwanzig (MZ;Zwanzig, 1964;Mori, 1965) formalism of statistical physics (Kondrashov et al, 2015). In addition to enhancing our understanding of the geophysical systems under consideration, EMR-MSM models have also been shown to be well suited for predictive purposes; e.g., they have considerable skill in predicting certain key variables associated with the El Niño-Southern Oscillation (Barnston et al, 2012;Chekroun et al, 2011) and the Madden-Julian Oscillation (Kondrashov et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

“…(1) is that the noise term η, which represents the unobserved variables, will typically be correlated with the state vector x. To overcome this problem, we adapt the recently developed non-Markovian data-driven closure models introduced by Kondrashov et al (2015) as follows.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Inverse stochastic–dynamic models for high-resolution Greenland ice core records

et al. 2017

Self Cite

View full text Add to dashboard Cite

Abstract. Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ 18 O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP), and we focus on the time interval 59-22 ka b2k. Our model reproduces the dynamical characteristics of both the δ 18 O and dust proxy records, including the millennial-scale Dansgaard-Oeschger variability, as well as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data, (ii) cubic drift terms, (iii) nonlinear coupling terms between the δ 18 O and dust time series, and (iv) non-Markovian contributions that represent short-term memory effects.

show abstract

Section: G(t S; X(s))ds + η(T)mentioning

confidence: 99%

Section: Approximating the Gle In Practicementioning

confidence: 99%

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Inverse stochastic–dynamic models for high-resolution Greenland ice core records

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

Stochastic modeling of decadal variability in ocean gyres

Kondrashov

Berloff

2015

Geophysical Research Letters

View full text Add to dashboard Cite

Decadal large-scale low-frequency variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper presents a novel fully data driven approach that addresses this challenge. Proposed is non-Markovian low-order methodology with stochastic closure and use of mode decomposition by multichannel Singular Spectrum Analysis. The multilayer stochastic linear model is obtained from the coarse-grained eddy-resolving ocean model solution, and with high accuracy it reproduces the main statistical properties of the decadal variability. The proposed methodology does not depend on the governing fluid dynamics equations and geometry of the problem, and it can be extended to other ocean models and ultimately to the real data. BackgroundMidlatitude atmosphere and ocean possess not only significant interannual variability but also several large-scale variability modes on decadal and interdecadal timescales: North Atlantic Oscillation, Atlantic Multidecadal Oscillation, and Pacific Decadal Oscillation. Oceanic evidence of these modes is found in the sea surface temperature [Hansen and Bezdek, 1996], hydrography [Qiu and Joyce, 1992], and altimetry [Qiu and Chen, 2005], and it is mostly expressed in structural changes of the eastward jet extensions and the adjacent recirculation zones of the main western boundary currents, such as the Gulf Stream and Kuroshio. Physical origins of these large-scale low-frequency variability (LFV) modes remain unclear, and it is not even known to what extent these origins are intrinsic atmospheric, intrinsic oceanic, or coupled oceanic-atmospheric. One of the reasons, why coupled ocean-atmosphere comprehensive general circulation models (GCMs) cannot distinguish between these scenarios, is inability of their oceanic model components to simulate mesoscale eddies and their impact on the large-scale currents accurately and for a long time. On the other hand, seasonally forced, eddy-resolving ocean-only GCMs exhibit significant intrinsic LFV variability of mesoscale activity [Penduff et al., 2011], intergyre heat transport [Hall et al., 2004], sea level height [Cabanes et al., 2006], western boundary currents [Taguchi et al., 2007], and meridional overturning circulation [Biastoch et al., 2008]. This suggests that not only significant part of the LFV is intrinsic to the ocean but also oceanic mesoscale eddies could play significant role in driving it.Present theoretical understanding of the intrinsic LFV of the ocean starts from the null hypothesis that the ocean integrates high-frequency atmospheric forcing and responds in terms of the red variability spectrum [Hasselman, 1976]. However, over the last 20 years it became evident that in the presence of stochastic, seasonal, or constant atmospheric forcing, the most significant intrinsic LFV of the ocean is not red but operates on interannual-to-interdecadal time scales. One idea is that this variability can be understood in terms of early bifurcations...

show abstract

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

Mohebujjaman

Rebholz

Iliescu

2018

Numerical Methods in Fluids

View full text Add to dashboard Cite

Summary We have recently proposed a data‐driven correction reduced‐order model (DDC‐ROM) framework for the numerical simulation of fluid flows, which can be formally written as follows. The new DDC‐ROM was constructed by using reduced‐order model spatial filtering and data‐driven reduced‐order model closure modeling (for the Correction term) and was successfully tested in the numerical simulation of a two‐dimensional channel flow past a circular cylinder at Reynolds numbers Re = 100,Re = 500, and Re = 1000. In this paper, we propose a physically constrained DDC‐ROM (CDDC‐ROM), which aims at improving the physical accuracy of the DDC‐ROM. The new physical constraints require that the CDDC‐ROM operators satisfy the same type of physical laws (ie, the Correction term's linear component should be dissipative, and the Correction term's nonlinear component should conserve energy) as those satisfied by the fluid flow equations. To implement these physical constraints, in the data‐driven modeling step, we replace the unconstrained least squares problem with a constrained least squares problem. We perform a numerical investigation of the new CDDC‐ROM and standard DDC‐ROM for a two‐dimensional channel flow past a circular cylinder at Reynolds numbers Re = 100,Re = 500, and Re = 1000. To this end, we consider a reproductive regime as well as a predictive (ie, cross‐validation) regime in which we use as little as 50% of the original training data. The numerical investigation clearly shows that the new CDDC‐ROM is significantly more accurate than the DDC‐ROM in both regimes.

show abstract

Data-driven non-Markovian closure models

Cited by 121 publications

References 133 publications

Inverse stochastic–dynamic models for high-resolution Greenland ice core records

Inverse stochastic–dynamic models for high-resolution Greenland ice core records

Stochastic modeling of decadal variability in ocean gyres

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

Contact Info

Product

Resources

About