Strategic Monte Carlo And Variational Methods In Statistical Data Assimilation For Nonlinear Dynamical Systems
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Strategic Monte Carlo And Variational Methods In Statistical Data Assimilation For Nonlinear Dynamical Systems
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Author : Aleksandra Shirman
language : en
Publisher:
Release Date : 2018
Strategic Monte Carlo And Variational Methods In Statistical Data Assimilation For Nonlinear Dynamical Systems written by Aleksandra Shirman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Data Assimilation (DA) is a method through which information is extracted from measured quantities and with the help of a mathematical model is transferred through a probability distribution to unknown or unmeasured states and parameters characterizing the system of study. With an estimate of the model paramters, quantitative predictions may be made and compared to subsequent data. Many recent DA efforts rely on an probability distribution optimization that locates the most probable state and parameter values given a set of data. The procedure developed and demonstrated here extends the optimization by appending a biased random walk around the states and parameters of high probability to generate an estimate of the structure in state space of the probability density function (PDF). The estimate of the structure of the PDF will facilitate more accurate estimates of expectation values of means, standard deviations and higher moments of states and parameters that characterize the behavior of the system of study. The ability to calculate these expectation values will allow for an error bar or tolerance interval to be attached to each estimated state or parameter, in turn giving significance to any results generated. The estimation method's merits will be demonstrated on a simulated well known chaotic system, the Lorenz 96 system, and on a toy model of a neuron. In both situations the model system provides unique challenges for estimation: In chaotic systems any small error in estimation generates extremely large prediction errors while in neurons only one of the (at minimum) four dynamical variables can be measured leading to a small amount of data with which to work. This thesis will conclude with an exploration of the equivalence of machine learning and the formulation of statistical DA. The application of previous DA methods are demonstrated on the classic machine learning problem: the characterization of handwritten images from the MNIST data set. The results of this work are used to validate common assumptions in machine learning work such as the dependence of the quality of results on the amount of data presented and the size of the network used. Finally DA is proposed as a method through which to discern an 'ideal' network size for a set of given data which optimizes predictive capabilities while minimizing computational costs.
The Statistical Physics Of Data Assimilation And Machine Learning
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Author : Henry D. I. Abarbanel
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-17
The Statistical Physics Of Data Assimilation And Machine Learning written by Henry D. I. Abarbanel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-17 with Computers categories.
The theory of data assimilation and machine learning is introduced in an accessible manner for undergraduate and graduate students.
Data Assimilation And Control Theory And Applications In Life Sciences
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Author : Axel Hutt
language : en
Publisher: Frontiers Media SA
Release Date : 2019-08-16
Data Assimilation And Control Theory And Applications In Life Sciences written by Axel Hutt and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with categories.
The understanding of complex systems is a key element to predict and control the system’s dynamics. To gain deeper insights into the underlying actions of complex systems today, more and more data of diverse types are analyzed that mirror the systems dynamics, whereas system models are still hard to derive. Data assimilation merges both data and model to an optimal description of complex systems’ dynamics. The present eBook brings together both recent theoretical work in data assimilation and control and demonstrates applications in diverse research fields.
Nonlinear Dynamics And Statistics
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Author : Alistair I. Mees
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Dynamics And Statistics written by Alistair I. Mees and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
This book describes the state of the art in nonlinear dynamical reconstruction theory. The chapters are based upon a workshop held at the Isaac Newton Institute, Cambridge University, UK, in late 1998. The book's chapters present theory and methods topics by leading researchers in applied and theoretical nonlinear dynamics, statistics, probability, and systems theory. Features and topics: * disentangling uncertainty and error: the predictability of nonlinear systems * achieving good nonlinear models * delay reconstructions: dynamics vs. statistics * introduction to Monte Carlo Methods for Bayesian Data Analysis * latest results in extracting dynamical behavior via Markov Models * data compression, dynamics and stationarity Professionals, researchers, and advanced graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book a useful resource and guide to current developments in the subject.
Nonlinear Dynamics And Statistics
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Author : Alistair I Mees
language : en
Publisher:
Release Date : 2001-01-25
Nonlinear Dynamics And Statistics written by Alistair I Mees and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-25 with categories.
Data Assimilation
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Author : Kody Law
language : en
Publisher: Springer
Release Date : 2015-09-05
Data Assimilation written by Kody Law and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-05 with Mathematics categories.
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.
Data Assimilation Fundamentals
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Author : Geir Evensen
language : en
Publisher: Springer Nature
Release Date : 2022-04-22
Data Assimilation Fundamentals written by Geir Evensen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-22 with Science categories.
This open-access textbook's significant contribution is the unified derivation of data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes' theorem. Unique for this book is the "top-down" derivation of the assimilation methods. It starts from Bayes theorem and gradually introduces the assumptions and approximations needed to arrive at today's popular data-assimilation methods. This strategy is the opposite of most textbooks and reviews on data assimilation that typically take a bottom-up approach to derive a particular assimilation method. E.g., the derivation of the Kalman Filter from control theory and the derivation of the ensemble Kalman Filter as a low-rank approximation of the standard Kalman Filter. The bottom-up approach derives the assimilation methods from different mathematical principles, making it difficult to compare them. Thus, it is unclear which assumptions are made to derive an assimilation method and sometimes even which problem it aspires to solve. The book's top-down approach allows categorizing data-assimilation methods based on the approximations used. This approach enables the user to choose the most suitable method for a particular problem or application. Have you ever wondered about the difference between the ensemble 4DVar and the "ensemble randomized likelihood" (EnRML) methods? Do you know the differences between the ensemble smoother and the ensemble-Kalman smoother? Would you like to understand how a particle flow is related to a particle filter? In this book, we will provide clear answers to several such questions. The book provides the basis for an advanced course in data assimilation. It focuses on the unified derivation of the methods and illustrates their properties on multiple examples. It is suitable for graduate students, post-docs, scientists, and practitioners working in data assimilation.
Monte Carlo Strategies In Scientific Computing
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Author : Jun S. Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Monte Carlo Strategies In Scientific Computing written by Jun S. Liu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.
Data Assimilation
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Author : Geir Evensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-22
Data Assimilation written by Geir Evensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-22 with Science categories.
This book reviews popular data-assimilation methods, such as weak and strong constraint variational methods, ensemble filters and smoothers. The author shows how different methods can be derived from a common theoretical basis, as well as how they differ or are related to each other, and which properties characterize them, using several examples. Readers will appreciate the included introductory material and detailed derivations in the text, and a supplemental web site.
Bayesian Time Series Models
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Author : David Barber
language : en
Publisher: Cambridge University Press
Release Date : 2011-08-11
Bayesian Time Series Models written by David Barber and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Computers categories.
The first unified treatment of time series modelling techniques spanning machine learning, statistics, engineering and computer science.