Data-driven non-Markovian closure models

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

doi:10.1016/j.physd.2014.12.005

Data-driven non-Markovian closure models

Journal Article · Sun Mar 01 00:00:00 EST 2015 · Physica. D, Nonlinear Phenomena

DOI:https://doi.org/10.1016/j.physd.2014.12.005· OSTI ID:1197779

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

Not Available

View Journal Article

Sponsoring Organization:: USDOE

OSTI ID:: 1197779

Journal Information:: Physica. D, Nonlinear Phenomena, Journal Name: Physica. D, Nonlinear Phenomena Journal Issue: C Vol. 297; ISSN 0167-2789

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (92)

A mathematical framework for stochastic climate models Majda, Andrew J.; Timofeyev, Ilya; Vanden Eijnden, Eric Communications on Pure and Applied Mathematics, Vol. 54, Issue 8 https://doi.org/10.1002/cpa.1014	journal	January 2001
Low‐order stochastic model and “past‐noise forecasting” of the Madden‐Julian Oscillation Kondrashov, D.; Chekroun, M. D.; Robertson, A. W. Geophysical Research Letters, Vol. 40, Issue 19 https://doi.org/10.1002/grl.50991	journal	October 2013
Asymptotic stability in viscoelasticity Dafermos, Constantine M. Archive for Rational Mechanics and Analysis, Vol. 37, Issue 4 https://doi.org/10.1007/BF00251609	journal	January 1970
On the differential equations of species in competition Smale, S. Journal of Mathematical Biology, Vol. 3, Issue 1 https://doi.org/10.1007/BF00307854	journal	January 1976
Attractors for random dynamical systems Crauel, Hans; Flandoli, Franco Probability Theory and Related Fields, Vol. 100, Issue 3 https://doi.org/10.1007/BF01193705	journal	September 1994
Strange attractors in volterra equations for species in competition Arneodo, A.; Coullet, P.; Peyraud, J. Journal of Mathematical Biology, Vol. 14, Issue 2 https://doi.org/10.1007/BF01832841	journal	June 1982
Chaos in abstract kinetics: Two prototypes Rössler, Otto E. Bulletin of Mathematical Biology, Vol. 39, Issue 2 https://doi.org/10.1007/BF02462866	journal	March 1977
Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications Chekroun, Mickaël D.; Glatt-Holtz, Nathan E. Communications in Mathematical Physics, Vol. 316, Issue 3 https://doi.org/10.1007/s00220-012-1515-y	journal	July 2012
Prediction from Partial Data, Renormalization, and Averaging Chorin, Alexandre J.; Hald, Ole H.; Kupferman, Raz Journal of Scientific Computing, Vol. 28, Issue 2-3 https://doi.org/10.1007/s10915-006-9089-5	journal	April 2006
Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach Wouters, Jeroen; Lucarini, Valerio Journal of Statistical Physics, Vol. 151, Issue 5 https://doi.org/10.1007/s10955-013-0726-8	journal	March 2013
Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space Maas, U.; Pope, S. B. Combustion and Flame, Vol. 88, Issue 3-4 https://doi.org/10.1016/0010-2180(92)90034-M	journal	March 1992
On the kinetics of the approach to equilibrium Prigonine, I.; Résibois, P. Physica, Vol. 27, Issue 7 https://doi.org/10.1016/0031-8914(61)90008-8	journal	July 1961
On the identity of three generalized master equations Zwanzig, Robert Physica, Vol. 30, Issue 6 https://doi.org/10.1016/0031-8914(64)90102-8	journal	June 1964
Extracting qualitative dynamics from experimental data Broomhead, D. S.; King, Gregory P. Physica D: Nonlinear Phenomena, Vol. 20, Issue 2-3 https://doi.org/10.1016/0167-2789(86)90031-X	journal	June 1986
The reduction of complex dynamical systems using principal interaction patterns Kwasniok, F. Physica D: Nonlinear Phenomena, Vol. 92, Issue 1-2 https://doi.org/10.1016/0167-2789(95)00280-4	journal	April 1996
Multilayer feedforward networks are universal approximators Hornik, Kurt; Stinchcombe, Maxwell; White, Halbert Neural Networks, Vol. 2, Issue 5 https://doi.org/10.1016/0893-6080(89)90020-8	journal	January 1989
El Niño and health Kovats, R. Sari; Bouma, Menno J.; Hajat, Shakoor The Lancet, Vol. 362, Issue 9394 https://doi.org/10.1016/S0140-6736(03)14695-8	journal	November 2003
Optimal prediction with memory Chorin, Alexandre J.; Hald, Ole H.; Kupferman, Raz Physica D: Nonlinear Phenomena, Vol. 166, Issue 3-4 https://doi.org/10.1016/S0167-2789(02)00446-3	journal	June 2002
Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena Majda, Andrew J.; Kramer, Peter R. Physics Reports, Vol. 314, Issue 4-5 https://doi.org/10.1016/S0370-1573(98)00083-0	journal	June 1999
A review on estimation of stochastic differential equations for pharmacokinetic/pharmacodynamic models Donnet, Sophie; Samson, Adeline Advanced Drug Delivery Reviews, Vol. 65, Issue 7 https://doi.org/10.1016/j.addr.2013.03.005	journal	June 2013
Probing chaos and biodiversity in a simple competition model Roques, Lionel; Chekroun, Mickaël D. Ecological Complexity, Vol. 8, Issue 1 https://doi.org/10.1016/j.ecocom.2010.08.004	journal	March 2011
An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models Harlim, John; Mahdi, Adam; Majda, Andrew J. Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.10.025	journal	January 2014
Random attractors for a class of stochastic partial differential equations driven by general additive noise Gess, Benjamin; Liu, Wei; Röckner, Michael Journal of Differential Equations, Vol. 251, Issue 4-5 https://doi.org/10.1016/j.jde.2011.02.013	journal	August 2011
Fitting SDE models to nonlinear Kac–Zwanzig heat bath models Kupferman, R.; Stuart, A. M. Physica D: Nonlinear Phenomena, Vol. 199, Issue 3-4 https://doi.org/10.1016/j.physd.2004.04.011	journal	December 2004
A comparative study of two stochastic mode reduction methods Stinis, Panagiotis Physica D: Nonlinear Phenomena, Vol. 213, Issue 2 https://doi.org/10.1016/j.physd.2005.11.010	journal	January 2006
Graphical models for statistical inference and data assimilation Ihler, Alexander T.; Kirshner, Sergey; Ghil, Michael Physica D: Nonlinear Phenomena, Vol. 230, Issue 1-2 https://doi.org/10.1016/j.physd.2006.08.023	journal	June 2007
Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance Strounine, K.; Kravtsov, S.; Kondrashov, D. Physica D: Nonlinear Phenomena, Vol. 239, Issue 3-4 https://doi.org/10.1016/j.physd.2009.10.013	journal	February 2010
Stochastic climate dynamics: Random attractors and time-dependent invariant measures Chekroun, Mickaël D.; Simonnet, Eric; Ghil, Michael Physica D: Nonlinear Phenomena, Vol. 240, Issue 21 https://doi.org/10.1016/j.physd.2011.06.005	journal	October 2011
Transition networks for modeling the kinetics of conformational change in macromolecules Noé, Frank; Fischer, Stefan Current Opinion in Structural Biology, Vol. 18, Issue 2 https://doi.org/10.1016/j.sbi.2008.01.008	journal	April 2008
Reduction of a Model Describing Ozone Oscillations in the Troposphere: Example of an Algorithmic Approach to Model Reduction in Atmospheric Chemistry Kalachev, Leonid V.; Field, Richard J. Journal of Atmospheric Chemistry, Vol. 39, Issue 1, p. 65-93 https://doi.org/10.1023/A:1010649217616	journal	May 2001
Fractional Kinetics in Kac–Zwanzig Heat Bath Models Kupferman, Raz Journal of Statistical Physics, Vol. 114, Issue 1/2 https://doi.org/10.1023/B:JOSS.0000003113.22621.f0	journal	January 2004
Advanced spectral methods for climatic time series Ghil, M. Reviews of Geophysics, Vol. 40, Issue 1 https://doi.org/10.1029/2000RG000092	journal	January 2002
Experimental forecasts of El Niño Cane, Mark A.; Zebiak, Stephen E.; Dolan, Sean C. Nature, Vol. 321, Issue 6073 https://doi.org/10.1038/321827a0	journal	June 1986
Civil conflicts are associated with the global climate Hsiang, Solomon M.; Meng, Kyle C.; Cane, Mark A. Nature, Vol. 476, Issue 7361 https://doi.org/10.1038/nature10311	journal	August 2011
Ensemble Method in the Theory of Irreversibility Zwanzig, Robert The Journal of Chemical Physics, Vol. 33, Issue 5 https://doi.org/10.1063/1.1731409	journal	November 1960
Markov models of molecular kinetics: Generation and validation Prinz, Jan-Hendrik; Wu, Hao; Sarich, Marco The Journal of Chemical Physics, Vol. 134, Issue 17 https://doi.org/10.1063/1.3565032	journal	May 2011
Applied Koopmanism Budišić, Marko; Mohr, Ryan; Mezić, Igor Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, Issue 4 https://doi.org/10.1063/1.4772195	journal	December 2012
Optimal prediction and the rate of decay for solutions of the Euler equations in two and three dimensions Hald, O. H.; Stinis, P. Proceedings of the National Academy of Sciences, Vol. 104, Issue 16 https://doi.org/10.1073/pnas.0700084104	journal	April 2007
Predicting stochastic systems by noise sampling, and application to the El Nino-Southern Oscillation Chekroun, M. D.; Kondrashov, D.; Ghil, M. Proceedings of the National Academy of Sciences, Vol. 108, Issue 29 https://doi.org/10.1073/pnas.1015753108	journal	July 2011
Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances Chekroun, Mickaël David; Neelin, J. David; Kondrashov, Dmitri Proceedings of the National Academy of Sciences, Vol. 111, Issue 5 https://doi.org/10.1073/pnas.1321816111	journal	January 2014
Optimal prediction and the Mori-Zwanzig representation of irreversible processes Chorin, A. J.; Hald, O. H.; Kupferman, R. Proceedings of the National Academy of Sciences, Vol. 97, Issue 7 https://doi.org/10.1073/pnas.97.7.2968	journal	March 2000
Identification of MIMO non-linear systems using a forward-regression orthogonal estimator Billings, S. A.; Chen, S.; Korenberg, M. J. International Journal of Control, Vol. 49, Issue 6 https://doi.org/10.1080/00207178908559767	journal	June 1989
Large deviations analysis of reflected diffusions and constrained stochastic approximation algorithms in convex sets ^† Dupuis, Paul Stochastics, Vol. 21, Issue 1 https://doi.org/10.1080/17442508708833451	journal	May 1987
Successive Refinements in Long‐Term Integrations of Planetary Orbits Varadi, F.; Runnegar, B.; Ghil, M. The Astrophysical Journal, Vol. 592, Issue 1 https://doi.org/10.1086/375560	journal	July 2003
Systems of differential equations which are competitive or cooperative: III. Competing species Hirsch, M. W. Nonlinearity, Vol. 1, Issue 1 https://doi.org/10.1088/0951-7715/1/1/003	journal	February 1988
Extracting macroscopic dynamics: model problems and algorithms Givon, Dror; Kupferman, Raz; Stuart, Andrew Nonlinearity, Vol. 17, Issue 6 https://doi.org/10.1088/0951-7715/17/6/R01	journal	August 2004
Chaos in low-dimensional Lotka–Volterra models of competition Vano, J. A.; Wildenberg, J. C.; Anderson, M. B. Nonlinearity, Vol. 19, Issue 10 https://doi.org/10.1088/0951-7715/19/10/006	journal	September 2006
A note on diffusion limits of chaotic skew-product flows Melbourne, I.; Stuart, A. M. Nonlinearity, Vol. 24, Issue 4 https://doi.org/10.1088/0951-7715/24/4/018	journal	March 2011
Physics constrained nonlinear regression models for time series Majda, Andrew J.; Harlim, John Nonlinearity, Vol. 26, Issue 1 https://doi.org/10.1088/0951-7715/26/1/201	journal	November 2012
On chaos in Lotka–Volterra systems: an analytical approach Kozlov, Vladimir; Vakulenko, Sergey Nonlinearity, Vol. 26, Issue 8 https://doi.org/10.1088/0951-7715/26/8/2299	journal	July 2013
On modelling physical systems with stochastic models: diffusion versus Lévy processes Penland, Cécile; Ewald, Brian D. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 366, Issue 1875 https://doi.org/10.1098/rsta.2008.0051	journal	May 2008
Data-based parameter estimation of generalized multidimensional Langevin processes Horenko, Illia; Hartmann, Carsten; Schütte, Christof Physical Review E, Vol. 76, Issue 1 https://doi.org/10.1103/PhysRevE.76.016706	journal	July 2007
Usage of the Mori-Zwanzig method in time series analysis Niemann, Markus; Laubrich, Thomas; Olbrich, Eckehard Physical Review E, Vol. 77, Issue 1 https://doi.org/10.1103/PhysRevE.77.011117	journal	January 2008
Sparse model from optimal nonuniform embedding of time series Nichkawde, Chetan Physical Review E, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevE.89.042911	journal	April 2014
Ergodic theory of chaos and strange attractors Eckmann, J. -P.; Ruelle, D. Reviews of Modern Physics, Vol. 57, Issue 3 https://doi.org/10.1103/RevModPhys.57.617	journal	July 1985
A new algorithm for linear and nonlinear ARMA model parameter estimation using affine geometry [and application to blood flow/pressure data] Lu, Sheng; Ju, Ki Hwan; Chon, K. H. IEEE Transactions on Biomedical Engineering, Vol. 48, Issue 10, p. 1116-1124 https://doi.org/10.1109/10.951514	journal	October 2001
Multiresolution Markov models for signal and image processing Willsky, A. S. Proceedings of the IEEE, Vol. 90, Issue 8 https://doi.org/10.1109/JPROC.2002.800717	journal	August 2002
Low-order stellar dynamo models: Low-order stellar dynamo models Wilmot-Smith, A. L.; Martens, P. C. H.; Nandy, D. Monthly Notices of the Royal Astronomical Society, Vol. 363, Issue 4 https://doi.org/10.1111/j.1365-2966.2005.09514.x	journal	September 2005
Global Stability in Ecological Systems with Continuous Time Delay Wörz-Busekros, Angelika SIAM Journal on Applied Mathematics, Vol. 35, Issue 1 https://doi.org/10.1137/0135011	journal	July 1978
Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets Hirsch, Morris W. SIAM Journal on Mathematical Analysis, Vol. 13, Issue 2 https://doi.org/10.1137/0513013	journal	March 1982
Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere Hirsch, Morris W. SIAM Journal on Mathematical Analysis, Vol. 16, Issue 3 https://doi.org/10.1137/0516030	journal	May 1985
Systems of Differential Equations That are Competitive or Cooperative. IV: Structural Stability in Three-Dimensional Systems Hirsch, Morris W. SIAM Journal on Mathematical Analysis, Vol. 21, Issue 5 https://doi.org/10.1137/0521067	journal	September 1990
Higher Order Mori–Zwanzig Models for the Euler Equations Stinis, Panagiotis Multiscale Modeling & Simulation, Vol. 6, Issue 3 https://doi.org/10.1137/06066504X	journal	January 2007
The Quasi-Steady-State Assumption: A Case Study in Perturbation Segel, Lee A.; Slemrod, Marshall SIAM Review, Vol. 31, Issue 3 https://doi.org/10.1137/1031091	journal	September 1989
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. SIAM Journal on Numerical Analysis, Vol. 40, Issue 3 https://doi.org/10.1137/S0036142901389530	journal	January 2002
On Quantum Theory of Transport Phenomena: Steady Diffusion Nakajima, Sadao Progress of Theoretical Physics, Vol. 20, Issue 6 https://doi.org/10.1143/PTP.20.948	journal	December 1958
Transport, Collective Motion, and Brownian Motion Mori, Hazime Progress of Theoretical Physics, Vol. 33, Issue 3 https://doi.org/10.1143/PTP.33.423	journal	March 1965
A Continued-Fraction Representation of the Time-Correlation Functions Mori, Hazime Progress of Theoretical Physics, Vol. 34, Issue 3 https://doi.org/10.1143/PTP.34.399	journal	September 1965
Prediction of Niño 3 Sea Surface Temperatures Using Linear Inverse Modeling Penland, Cécile; Magorian, Theresa Journal of Climate, Vol. 6, Issue 6 https://doi.org/10.1175/1520-0442(1993)006<1067:PONSST>2.0.CO;2	journal	June 1993
The Optimal Growth of Tropical Sea Surface Temperature Anomalies Penland, Cécile; Sardeshmukh, Prashant D. Journal of Climate, Vol. 8, Issue 8 https://doi.org/10.1175/1520-0442(1995)008<1999:TOGOTS>2.0.CO;2	journal	August 1995
A Linear Model of Wintertime Low-Frequency Variability. Part I: Formulation and Forecast Skill Winkler, Christopher R.; Newman, Matthew; Sardeshmukh, Prashant D. Journal of Climate, Vol. 14, Issue 24 https://doi.org/10.1175/1520-0442(2001)014<4474:ALMOWL>2.0.CO;2	journal	December 2001
Deterministic Nonperiodic Flow Lorenz, Edward N. Journal of the Atmospheric Sciences, Vol. 20, Issue 2 https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2	journal	March 1963
Internal Variability of an Energy-Balance Model with Delayed Albedo Effects Bhattacharya, K.; Ghil, M.; Vulis, I. L. Journal of the Atmospheric Sciences, Vol. 39, Issue 8 https://doi.org/10.1175/1520-0469(1982)039<1747:IVOAEB>2.0.CO;2	journal	August 1982
Multiple Flow Regimes in the Northern Hemisphere Winter. Part I: Methodology and Hemispheric Regimes Kimoto, Masahide; Ghil, Michael Journal of the Atmospheric Sciences, Vol. 50, Issue 16 https://doi.org/10.1175/1520-0469(1993)050<2625:MFRITN>2.0.CO;2	journal	August 1993
Multiple Flow Regimes in the Northern Hemisphere Winter. Part II: Sectorial Regimes and Preferred Transitions Kimoto, Masahide; Ghil, Michael Journal of the Atmospheric Sciences, Vol. 50, Issue 16 https://doi.org/10.1175/1520-0469(1993)050<2645:MFRITN>2.0.CO;2	journal	August 1993
Strategies for Model Reduction: Comparing Different Optimal Bases Crommelin, D. T.; Majda, A. J. Journal of the Atmospheric Sciences, Vol. 61, Issue 17 https://doi.org/10.1175/1520-0469(2004)061<2206:SFMRCD>2.0.CO;2	journal	September 2004
Global and Regional Scale Precipitation Patterns Associated with the El Niño/Southern Oscillation Ropelewski, C. F.; Halpert, M. S. Monthly Weather Review, Vol. 115, Issue 8 https://doi.org/10.1175/1520-0493(1987)115<1606:GARSPP>2.0.CO;2	journal	August 1987
Random Forcing and Forecasting Using Principal Oscillation Pattern Analysis Penland, Cecile Monthly Weather Review, Vol. 117, Issue 10 https://doi.org/10.1175/1520-0493(1989)117<2165:RFAFUP>2.0.CO;2	journal	October 1989
The Origin of Nonlinear Signatures of Planetary Wave Dynamics: Mean Phase Space Tendencies and Contributions from Non-Gaussianity Franzke, Christian; Majda, Andrew J.; Branstator, Grant Journal of the Atmospheric Sciences, Vol. 64, Issue 11 https://doi.org/10.1175/2006JAS2221.1	journal	November 2007
Signatures of Nonlinear Dynamics in an Idealized Atmospheric Model Kondrashov, Dmitri; Kravtsov, Sergey; Ghil, Michael Journal of the Atmospheric Sciences, Vol. 68, Issue 1 https://doi.org/10.1175/2010JAS3524.1	journal	January 2011
Skill of Real-Time Seasonal ENSO Model Predictions during 2002–11: Is Our Capability Increasing? Barnston, Anthony G.; Tippett, Michael K.; L'Heureux, Michelle L. Bulletin of the American Meteorological Society, Vol. 93, Issue 5 https://doi.org/10.1175/BAMS-D-11-00111.1	journal	May 2012
Predictability Associated with Nonlinear Regimes in an Atmospheric Model Peters, John M.; Kravtsov, Sergey; Schwartz, Nicholas T. Journal of the Atmospheric Sciences, Vol. 69, Issue 3 https://doi.org/10.1175/JAS-D-11-0168.1	journal	March 2012
Empirical Mode Reduction in a Model of Extratropical Low-Frequency Variability Kondrashov, D.; Kravtsov, S.; Ghil, M. Journal of the Atmospheric Sciences, Vol. 63, Issue 7 https://doi.org/10.1175/JAS3719.1	journal	July 2006
Reduced Atmospheric Models Using Dynamically Motivated Basis Functions Kwasniok, Frank Journal of the Atmospheric Sciences, Vol. 64, Issue 10 https://doi.org/10.1175/JAS4022.1	journal	October 2007
Multilevel Regression Modeling of Nonlinear Processes: Derivation and Applications to Climatic Variability Kravtsov, S.; Kondrashov, D.; Ghil, M. Journal of Climate, Vol. 18, Issue 21 https://doi.org/10.1175/JCLI3544.1	journal	November 2005
A Hierarchy of Data-Based ENSO Models Kondrashov, D.; Kravtsov, S.; Robertson, A. W. Journal of Climate, Vol. 18, Issue 21 https://doi.org/10.1175/JCLI3567.1	journal	November 2005
Cluster Analysis of Typhoon Tracks. Part II: Large-Scale Circulation and ENSO Camargo, Suzana J.; Robertson, Andrew W.; Gaffney, Scott J. Journal of Climate, Vol. 20, Issue 14 https://doi.org/10.1175/JCLI4203.1	journal	July 2007
Problem reduction, renormalization, and memory Chorin, Alexandre; Stinis, Panagiotis Communications in Applied Mathematics and Computational Science, Vol. 1, Issue 1 https://doi.org/10.2140/camcos.2006.1.1	journal	January 2006
On the prediction of ENSO: a study with a low-order Markov model Xue, Yan; Cane, M. A.; Zebiak, S. E. Tellus A: Dynamic Meteorology and Oceanography, Vol. 46, Issue 4 https://doi.org/10.3402/tellusa.v46i4.15641	journal	January 1994
Random attractors--general properties, existence and applications to stochastic bifurcation theory Reiner Schenk-Hoppé, Klaus Discrete & Continuous Dynamical Systems - A, Vol. 4, Issue 1 https://doi.org/10.3934/dcds.1998.4.99	journal	January 1998
Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operator D. Chekroun, Mickaël; Roux, Jean Discrete & Continuous Dynamical Systems - A, Vol. 33, Issue 9 https://doi.org/10.3934/dcds.2013.33.3957	journal	January 2013
Smooth Anosov flows: Correlation spectra and stability Butterley, Oliver; Liverani, Carlangelo Journal of Modern Dynamics, Vol. 1, Issue 2 https://doi.org/10.3934/jmd.2007.1.301	journal	January 2007

Similar Records

Nature of the nonequilibrium phase transition in the non-Markovian driven Dicke model

Journal Article · Tue Sep 22 20:00:00 EDT 2020 · Physical Review A · OSTI ID:1803839

Comparing different non-Markovianity measures in a driven qubit system

Journal Article · Fri Jan 14 23:00:00 EST 2011 · Physical Review. A · OSTI ID:21529034

Data-driven non-Markovian closure models

Citation Formats

References (92)

Similar Records

Related Subjects