Titlebook: Deep Learning in Multi-step Prediction of Chaotic Dynamics; From Deterministic M Matteo Sangiorgio,Fabio Dercole,Giorgio Guariso Book 2021

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https://doi.org/10.1007/978-3-030-94482-7Chaotic attractors; Neural network training; Recurrent neural networks; Henon systems; Exposure bias; env

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978-3-030-94481-0The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

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Lecture Notes in Computer ScienceThe forecasting of these dynamics has attracted the attention of many scientists since the discovery of chaos by Lorenz in the 1960s. In the last decades, machine learning techniques have shown a greater predictive accuracy than traditional tools from nonlinear time-series analysis. In particular, a

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Paria Shirani,Lingyu Wang,Mourad Debbabid by several kinds of deterministic nonlinear systems. We introduce the class of discrete-time autonomous systems so that an output time series can directly represent data measurements in a real system. The two basic concepts defining chaos are that of attractor—a bounded subset of the state space a

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M. L. Simoons,T. Boehmer,J. Roelandt,J. Poolre the prototypes of chaos in non-reversible and reversible systems, respectively, and two generalized Hénon maps, which represent cases of low- and high-dimensional hyperchaos. We also present a modified version of the traditional logistic map, introducing a slow periodic dynamic of the growth rate

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M. L. Simoons,T. Boehmer,J. Roelandt,J. Poolmore tangled in the prediction on a multiple-step horizon and consequently the task can be framed in different ways. For example, one can develop a single-step predictor to be used recursively along the forecasting horizon (recursive approach) or develop a multi-output model that directly forecasts

Mechanics

M. L. Simoons,T. Boehmer,J. Roelandt,J. Poolhe classical case of measurement noise by adding a random Gaussian signal of different intensity to the deterministic output of some archetypal chaotic systems. Then, we examine the critical case of structural noise, represented by the slow variation of the growth rate parameter of the logistic map.

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Prognostic Value of Stress Testingpecific information to ensure the reproducibility of a wide number of numerical experiments. A sensitivity analysis on some critical aspects is provided in order to prove the robustness of our setting. Considering the long-term behavior of the predictors, those trained for the one-step forecasting a

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Laurence Kay,André Rossi,Valdur Saks difficulty of their prediction. Our analysis shows that the LSTM predictor trained without teacher forcing is the most accurate approach in the forecasting of complex oscillatory time series. This predictor always provides the best accuracy in all the considered tasks, spanning a wide range of comp