複雑動態システムのモデリングと予測のための確率論的手法（第２版） Stochastic Methods for Modeling and Predicting Complex Dynamical Systems : Uncertainty Quantification, State Estimation, and Reduced-Order Models (Synthesis Lectures on Mathematics & Statistics) （2. Aufl. 2025. xvi, 225 S. XVI, 225 p. 42 illus., 39 illus. in color.）

Chen, Nan

SPRINGER, BERLIN; SPRINGER NATURE SWITZERLAND; SPRING（2025発売）

• 製本 Hardcover:ハードカバー版／ページ数 220 p.
• 言語 ENG
• 商品コード 9783031819230

Full Description

This Second Edition is an essential guide to understanding, modeling, and predicting complex dynamical systems using new methods with stochastic tools. Expanding upon the original book, the author covers a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. The author presents mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools. The book provides practical examples and motivations when introducing these tools, merging mathematics, statistics, information theory, computational science, and data science. The author emphasizes the balance between computational efficiency and modeling accuracy while equipping readers with the skills to choose and apply stochastic tools to a wide range of disciplines. This second edition includes updated discussion of combining stochastic models with machine learning and addresses several additional topics, including importance sampling, regression, and maximum likelihood estimate. The author also introduces a new chapter on optimal control.

Contents

Stochastic Toolkits.- Introduction to Information Theory.- Basic Stochastic Computational Methods.- Simple Gaussian and Non-Gaussian SDEs.- Data Assimilation.- Optimal Control.- Prediction.- Data-Driven Low-Order Stochastic Models.- Conditional Gaussian Nonlinear Systems.- Parameter Estimation with Uncertainty Quantification.- Combining Stochastic Models with Machine Learning.- Instruction Manual for the MATLAB Codes.