Class-oriented techniques for reconstruction of dynamics from time series

Безручко, Б. П.; Ponomarenko, V. I.; Смирнов, Д. А.; Sysoev, Ilya V.; Прохоров, М. Д.

doi:10.1016/j.chaos.2021.110972

Cited by 3 publications

(3 citation statements)

References 107 publications

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“…However, in general case, τ i can be unknown. To solve this problem, special techniques can be used [39]. The proposed approach can also solve this problem by constructing the dependency of target function on the trial delay time θ i .…”

Section: Methodsmentioning

confidence: 99%

Identification of Couplings in Adaptive Dynamical Networks of Time-Delayed Feedback Oscillators

et al. 2021

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An approach to solve the inverse problem of the reconstruction of the network of time-delay oscillators from their time series is proposed and studied in the case of the nonstationary connectivity matrix. Adaptive couplings have not been considered yet for this particular reconstruction problem. The problem of coupling identification is reduced to linear optimization of a specially constructed target function. This function is introduced taking into account the continuity of the nonlinear functions of oscillators and does not exploit the mean squared difference between the model and observed time series. The proposed approach allows us to minimize the number of estimated parameters and gives asymptotically unbiased estimates for a large class of nonlinear functions. The approach efficiency is demonstrated for the network composed of time-delayed feedback oscillators with a random architecture of constant and adaptive couplings in the absence of a priori knowledge about the connectivity structure and its evolution. The proposed technique extends the application area of the considered class of methods.

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Section: Methodsmentioning

confidence: 99%

Identification of Couplings in Adaptive Dynamical Networks of Time-Delayed Feedback Oscillators

et al. 2021

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“…where △ is a positive singular value; U and V are left singular matrices and right singular matrices, respectively. (3) e useful signal components of the sequence data are separated from the noise, and larger singular values are selected to describe the trajectory matrix as follows [16]:…”

Section: Time Series Predictionmentioning

confidence: 99%

An Intelligent Prediction for Sports Industry Scale Based on Time Series Algorithm and Deep Learning

Liang

2022

Computational Intelligence and Neuroscience

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Aiming at some existing issues in the sports industry, the existing model is optimized by deep learning and time series theory based on the relevant algorithm, and the scale of the sports industry is analyzed and predicted by the model. The results show the following: (1) Based on the single-step prediction of time series, MNTS structural algorithm can be used to describe and study the sports industry scale with the single factor, and the correlation fitting degree is high. (2) Curves of different evaluation methods can include parts linear stage and nonlinear stage according to the magnitude of change. (3) Seen from the optimization model in this paper, the proposed method can describe both global and local trends of data. (4) It can be seen from the prediction curve that the overall state of fluctuation indicates that time will have a great impact on the relevant scale of the sports industry. Compared with single-step prediction, the accuracy of multistep prediction is higher, and the multistep prediction model based on time series can well characterize and predict the scale of the sports industry. By using the relevant time algorithm, the sports industry scale can be predicted and analyzed so as to provide theoretical support for the formulation and implementation of relevant policies.

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“…Another method is to use a predefined restricted number of models and a special version of the Bayesian information criterion [17] to determine the best model. The degree of prior knowledge is also discussed outside the context of likelihood methods in a review written by the Saratov group [18].…”

Section: Introductionmentioning

confidence: 99%

Preprocessing algorithms for the estimation of ordinary differential equation models with polynomial nonlinearities

Strebel¹

2023

Nonlinear Dyn

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The data analysis task of determining a model for an ordinary differential equation (ODE) system from given noisy solution data is addressed. Since modeling with ODE is ubiquitous in science and technology, finding ODE models from data is of paramount importance. Based on a previously published parameter estimation method for ODE models, four related model estimation algorithms were developed. The algorithms are tested for over 20 different polynomial ordinary equation systems comprising 60 equations at various noise levels. Two algorithms frequently compute the correct model. They are compared to the prominent SINDy-family for those SINDy-algorithms that have simple default hyperparameters. This demonstrates that they are comparable to SINDy and more resilient towards noise than the tested SINDy algorithms.

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Class-oriented techniques for reconstruction of dynamics from time series

Cited by 3 publications

References 107 publications

Identification of Couplings in Adaptive Dynamical Networks of Time-Delayed Feedback Oscillators

Identification of Couplings in Adaptive Dynamical Networks of Time-Delayed Feedback Oscillators

An Intelligent Prediction for Sports Industry Scale Based on Time Series Algorithm and Deep Learning

Preprocessing algorithms for the estimation of ordinary differential equation models with polynomial nonlinearities

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