Название: Stochastic Methods for Modeling and Predicting Complex Dynamical Systems: Uncertainty Quantification, State Estimation, and Reduced-Order Models
Автор: Nan Chen
Издательство: Springer
Серия: Synthesis Lectures on Mathematics & Statistics
Год: 2023
Страниц: 208
Язык: английский
Формат: pdf (true), epub
Размер: 27.2 MB
This book enables readers to understand, model, and predict complex dynamical systems using new methods with stochastic tools. The author presents a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. An emphasis is placed on the balance between computational efficiency and modeling accuracy, providing readers with ideas to build useful models in practice. Successful modeling of complex systems requires a comprehensive use of qualitative and quantitative modeling approaches, novel efficient computational methods, physical intuitions and thinking, as well as rigorous mathematical theories. As such, mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools are presented. Both theoretical and numerical approaches are included, allowing readers to choose suitable methods in different practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational science, and Data Science. Machine Learning has become a prevalent and powerful tool to advance the modeling and forecast of many complex dynamical systems. One of the main advantages of machine learning is its computational efficiency. In fact, once a Machine Learning model is trained, the forecast utilizing such a model is often much cheaper than numerically integrating a traditional high-dimensional nonlinear dynamical model made up of explicit parametric terms.