Uncertainty Quantification and Stochastic Modeling with Matlab Hardcover

Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences.

Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones.

This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlab® illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study.

• Discusses the main ideas of Stochastic Modeling and Uncertainty Quantification using Functional Analysis
• Details listings of Matlab® programs implementing the main methods which complete the methodological presentation by a practical implementation
• Construct your own implementations from provided worked examples

不確定性量化（UQ）是一個相對新的研究領域，描述了在模擬問題和模型中不確定性、變異性和誤差的影響的定量描述的方法和途徑。它正在迅速成為一個越來越重要的領域，在統計學、數學、概率和工程學中有許多實際應用，同時也在自然科學領域中有應用。

迄今為止，關於這個主題的文獻主要基於多項式混沌，這在考慮不同類型的近似時存在困難，並且不能提供方法的統一介紹。此外，這種描述也沒有考慮到確定性問題或無窮維問題。

本書提供了一個統一、實用和全面的介紹，闡述了用於數值模型中不確定性效應的主要技術以及在數值問題中的應用。特別是，介紹了在線性和非線性方程組、微分方程、優化和可靠性方面的應用。還討論了使用隨機方法處理確定性數值問題的應用。Matlab®演示了這些方法的實施，使本書適合作為教材和自學使用。

本書討論了使用函數分析的隨機建模和不確定性量化的主要思想，並提供了實現主要方法的Matlab®程序清單，以實際實現方法的方法論介紹。您可以根據提供的實例構建自己的實現。