Matlab packages: 

  1. Multilayer Stochastic Modeling (MSM) 
  2. Past-Noise Forecasting (PNF)
  3. Data-adaptive Harmonic Decomposition (DAHD)    


These tools demonstrate several data-driven nonlinear stochastic-dynamic methods for analysis, modeling and prediction of datasets from partially-observed systems.   

  1. Empirical Model Reduction [Kondrashov et al, 2005, Kravtsov et al. 2009] within a general class of nonlinear Multilayer Stochastic Models (MSM) with memory effects and complex noise structure [Kondrashov et al. 2015, Ghil et al. 2018]. 
  2.  “Past-noise forecasting” [Chekroun, Kondrashov and Ghil et al. 2011]. 
  3. Data-adaptive Harmonic Decomposition [Chekroun and Kondrashov, 2017; Kondrashov et al. 2018, Kondrashov et al. 2020] for identification of coherent spatio-temporal modes in a shorty and noisy dataset. 





Kondrashov, D., Ryzhov, E.A. and P.S. Berloff, 2020: Data-adaptive harmonic analysis of oceanic waves and turbulent flows, Chaos, 30, 061105, doi:10.1063/5.0012077.

Kondrashov, D., M. D. Chekroun, X. Yuan, and M. Ghil, 2018: Data-adaptive Harmonic Decomposition and Stochastic Modeling of Arctic Sea Ice, In: Tsonis A. (eds) Advances in Nonlinear Geosciences. Springer, doi:10.1007/978-3-319-58895-7_10.

Ghil, M., A. Groth, D. Kondrashov, and A.W. Robertson, 2018: Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view.,In The Gap between Weather and Climate Forecasting: Sub-Seasonal to Seasonal Prediction.  A.W . Robertson and F. Vitart (eds), Elsevier.

Chekroun, M. D., and D. Kondrashov, 2017: Data-adaptive harmonic spectra and multilayer Stuart-Landau models, Chaos, 27, 093110: doi:10.1063/1.4989400, HAL preprint.

Kondrashov, D., M.D. Chekroun, and M. Ghil, 2015: Data-driven non-Markovian closure models, Physica D, 297, 33-55, doi:10.1016/j.physd.2014.12.005.

 Chekroun, M. D., D. Kondrashov and M. Ghil, 2011: Predicting stochastic systems by noise sampling, and application to the El Niño-Southern Oscillation, Proc. Nat. Acad. Sciences, 108 (29), 11766–11771, doi: 10.1073/pnas.1015753108

Kravtsov S., D. Kondrashov, and M. Ghil, 2005:  Multi-level regression modeling of nonlinear processes: Derivation and applications to climatic variability.  J. Climate, 18, 4404–4424, doi: 10.1175/JCLI3544.1