Long Range Predictability Of High Dimensional Chaotic Dynamics

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Long Range Predictability of High Dimensional Chaotic Dynamics

This thesis concerns the long range prediction of high dimensional chaotic systems. To this end, I investigate the important relationship between predictability and non-uniformity of information loss throughout the state space of a chaotic system. I introduce a genetic algorithm to build predictive models by exploiting this nonuniformity. The algorithm searches for the regions of state space which remain most predictable for a given time into the future. I use the algorithm to investigate the predictability of both model chaotic systems and physical data from a fluid flow experiment.
Deep Learning in Multi-step Prediction of Chaotic Dynamics

The book represents the first attempt to systematically deal with the use of deep neural networks to forecast chaotic time series. Differently from most of the current literature, it implements a multi-step approach, i.e., the forecast of an entire interval of future values. This is relevant for many applications, such as model predictive control, that requires predicting the values for the whole receding horizon. Going progressively from deterministic models with different degrees of complexity and chaoticity to noisy systems and then to real-world cases, the book compares the performances of various neural network architectures (feed-forward and recurrent). It also introduces an innovative and powerful approach for training recurrent structures specific for sequence-to-sequence tasks. The book also presents one of the first attempts in the context of environmental time series forecasting of applying transfer-learning techniques such as domain adaptation.
High-Dimensional Chaotic and Attractor Systems

Author: Vladimir G. Ivancevic
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-02-06
This graduate–level textbook is devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics. From introductory material on low-dimensional attractors and chaos, the text explores concepts including Poincaré’s 3-body problem, high-tech Josephson junctions, and more.