The impossibility to use the MCMC (Markov chain Monte Carlo) methods for long noisy chaotic time ... more The impossibility to use the MCMC (Markov chain Monte Carlo) methods for long noisy chaotic time series (TS) (due to high computational complexity) is a serious limitation for reconstruction of dynamical systems (DSs). In particular, it does not allow one to use the universal Bayesian approach for reconstruction of a DS in the most interesting case of the unknown evolution operator of the system. We propose a technique that makes it possible to use the MCMC methods for Bayesian reconstruction of a DS from noisy chaotic TS of arbitrary long duration.
An approach to the long-term prognosis of qualitative behavior of a dynamic system (DS) is propos... more An approach to the long-term prognosis of qualitative behavior of a dynamic system (DS) is proposed, which is based on the nonlinear-dynamical analysis of a weakly nonstationary chaotic time series (TS). A method for constructing prognostic models using the observed evolution of a single dynamic variable is described, which employs the proposed approach for prediction of bifurcations of low-dimensional DSs.
We present an approach to predicting regime transitions in the climate system's behavior fro... more We present an approach to predicting regime transitions in the climate system's behavior from observed time series. This approach is based on constructing reduced-order stochastic models of a discrete evolution operator from the observations. These models are given by the superposition of a deterministic and a stochastic component; the latter is sought as a state-dependent random function. Artificial neural networks with certain priors are used for the parameterization of the models. Model learning takes place in a subspace of the ...
The impossibility to use the MCMC (Markov chain Monte Carlo) methods for long noisy chaotic time ... more The impossibility to use the MCMC (Markov chain Monte Carlo) methods for long noisy chaotic time series (TS) (due to high computational complexity) is a serious limitation for reconstruction of dynamical systems (DSs). In particular, it does not allow one to use the universal Bayesian approach for reconstruction of a DS in the most interesting case of the unknown evolution operator of the system. We propose a technique that makes it possible to use the MCMC methods for Bayesian reconstruction of a DS from noisy chaotic TS of arbitrary long duration.
An approach to the long-term prognosis of qualitative behavior of a dynamic system (DS) is propos... more An approach to the long-term prognosis of qualitative behavior of a dynamic system (DS) is proposed, which is based on the nonlinear-dynamical analysis of a weakly nonstationary chaotic time series (TS). A method for constructing prognostic models using the observed evolution of a single dynamic variable is described, which employs the proposed approach for prediction of bifurcations of low-dimensional DSs.
We present an approach to predicting regime transitions in the climate system's behavior fro... more We present an approach to predicting regime transitions in the climate system's behavior from observed time series. This approach is based on constructing reduced-order stochastic models of a discrete evolution operator from the observations. These models are given by the superposition of a deterministic and a stochastic component; the latter is sought as a state-dependent random function. Artificial neural networks with certain priors are used for the parameterization of the models. Model learning takes place in a subspace of the ...
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Papers by E. Loskutov