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Author: Matteo Sangiorgio Publisher: Springer Nature ISBN: 3030944824 Category : Mathematics Languages : en Pages : 111
Book Description
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.
Author: Matteo Sangiorgio Publisher: Springer Nature ISBN: 3030944824 Category : Mathematics Languages : en Pages : 111
Book Description
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.
Author: Howell Tong Publisher: World Scientific ISBN: 9814549762 Category : Languages : en Pages : 356
Book Description
It is now generally recognised that very simple dynamical systems can produce apparently random behaviour. In the last couple of years, attention has turned to focus on the flip side of this coin: random-looking time series (or random-looking patterns in space) may indeed be the result of very complicated processes or “real noise”, but they may equally well be produced by some very simple mechanism (a low-dimensional attractor). In either case, a long-term prediction will be possible only in probabilistic terms. However, in the very short term, random systems will still be unpredictable but low-dimensional chaotic ones may be predictable (appearances to the contrary). The Royal Society held a two-day discussion meeting on topics covering diverse fields, including biology, economics, geophysics, meteorology, statistics, epidemiology, earthquake science and many others. Each topic was covered by a leading expert in the field. The meeting dealt with different basic approaches to the problem of chaos and forecasting, and covered applications to nonlinear forecasting of both artificially-generated time series and real data from context in the above-mentioned diverse fields. This book marks a rather special and rare occasion on which prominent scientists from different areas converge on the same theme. It forms an informative introduction to the science of chaos, with special reference to real data. Contents:Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective (B Cheng & H Tong)A Theory of Correlation Dimension for Stationary Time Series (C D Cutler)On Prediction and Chaos in Stochastic Systems (Q W Yao & H Tong)Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic (L A Smith)A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series (R C L Wolff)Chaos and Nonlinear Forecastability in Economics and Finance (B LeBaron)Paradigm Change in Prediction (A S Weigend)and other papers Readership: Mathematicians, economists, statisticians and nonlinear scientists. keywords: “… useful and recommended for forecast researchers striving for a more realistic methodology that goes substantially beyond conventional statistical theory.” M A Kaboudan
Author: Juan C. Vallejo Publisher: Springer ISBN: 3319518933 Category : Science Languages : en Pages : 136
Book Description
This book is primarily concerned with the computational aspects of predictability of dynamical systems – in particular those where observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for instance in celestial mechanics, one is confronted with the observation and modeling of systems without the possibility of altering the key parameters of the objects studied. Therefore, the numerical simulations offer an essential tool for analyzing these systems. With the widespread use of computer simulations to solve complex dynamical systems, the reliability of the numerical calculations is of ever-increasing interest and importance. This reliability is directly related to the regularity and instability properties of the modeled flow. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the finite-time Lyapunov exponents approach. The method is illustrated using a number of well-known continuous dynamical systems, including the Contopoulos, Hénon-Heiles and Rössler systems. To help students and newcomers quickly learn to apply these techniques, the appendix provides descriptions of the algorithms used throughout the text and details how to implement them in order to solve a given continuous dynamical system.
Author: Foster Morrison Publisher: Courier Corporation ISBN: 0486131718 Category : Mathematics Languages : en Pages : 418
Book Description
This text illustrates the roles of statistical methods, coordinate transformations, and mathematical analysis in mapping complex, unpredictable dynamical systems. It describes the benefits and limitations of the available modeling tools, showing engineers and scientists how any system can be rendered simpler and more predictable. Written by a well-known authority in the field, this volume employs practical examples and analogies to make models more meaningful. The more universal methods appear in considerable detail, and advanced dynamic principles feature easy-to-understand examples. The text draws careful distinctions between mathematical abstractions and observable realities. Additional topics include the role of pure mathematics, the limitations of numerical methods, forecasting in the presence of chaos and randomness, and dynamics without calculus. Specialized techniques and case histories are coordinated with a carefully selected and annotated bibliography. The original edition was a Library of Science Main Selection in May, 1991. This new Dover edition features corrections by the author and a new Preface.
Author: Royal Society (Great Britain). Discussion Meeting Publisher: World Scientific Publishing Company Incorporated ISBN: 9789810221263 Category : Science Languages : en Pages : 345
Author: Flavio Lorenzelli Publisher: CRC Press ISBN: 0203214587 Category : Science Languages : en Pages : 236
Book Description
The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.
Author: Leonard Smith Publisher: OUP Oxford ISBN: 0191579432 Category : Science Languages : en Pages : 200
Book Description
Chaos exists in systems all around us. Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Author: Luigi Piroddi Publisher: Springer Nature ISBN: 3030859185 Category : Technology & Engineering Languages : en Pages : 151
Book Description
This open access book presents thirteen outstanding doctoral dissertations in Information Technology from the Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy. Information Technology has always been highly interdisciplinary, as many aspects have to be considered in IT systems. The doctoral studies program in IT at Politecnico di Milano emphasizes this interdisciplinary nature, which is becoming more and more important in recent technological advances, in collaborative projects, and in the education of young researchers. Accordingly, the focus of advanced research is on pursuing a rigorous approach to specific research topics starting from a broad background in various areas of Information Technology, especially Computer Science and Engineering, Electronics, Systems and Control, and Telecommunications. Each year, more than 50 PhDs graduate from the program. This book gathers the outcomes of the thirteen best theses defended in 2020-21 and selected for the IT PhD Award. Each of the authors provides a chapter summarizing his/her findings, including an introduction, description of methods, main achievements and future work on the topic. Hence, the book provides a cutting-edge overview of the latest research trends in Information Technology at Politecnico di Milano, presented in an easy-to-read format that will also appeal to non-specialists.
Author: Matteo Sangiorgio
Author: Matteo Sangiorgio
Author: Howell Tong
Author: B. Grenfell
Author: Juan C. Vallejo
Author: Foster Morrison
Author: Royal Society (Great Britain). Discussion Meeting
Author: Flavio Lorenzelli
Author: Leonard Smith
Author: H. Tong
Author: Luigi Piroddi