Titlebook: Stochastic Methods for Modeling and Predicting Complex Dynamical Systems; Uncertainty Quantifi Nan Chen Textbook 2023 The Editor(s) (if app

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1938-1743 t practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational sc978-3-031-22251-1978-3-031-22249-8Series ISSN 1938-1743 Series E-ISSN 1938-1751

Antecedent

Introduction to Information Theory,e PDFs and coarse-grained statistical models, will also be presented with concrete examples. In addition, the relationship between the information criteria and the path-wise measurements will be developed, which illustrates the necessity of adopting the former in studying many complex turbulent syst

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Simple Gaussian and Non-Gaussian SDEs,mplex nonlinear systems, closure methods are introduced, which are useful tools for approximating the moment equations in the presence of strong nonlinearity. Finally, a family of nonlinear SDEs with exactly solvable conditional moments is developed, aiming at providing a powerful tool to approximat

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Prediction,uation-dissipation theory (FDT) is introduced to facilitate the prediction of model response to external perturbations, which outweighs direct methods in terms of computational efficiency and accuracy. Finally, an information criterion is introduced to find the direction of the perturbation that lea

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Parameter Estimation with Uncertainty Quantification,te variables. Finally, learning the structure and parameters of complex dynamical systems utilizing data is discussed. In addition to the constrained optimization via an L1 regularization, the sparse identification of the model structure can also be carried out in light of information theory. The la

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Nan Chenmarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also