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. In addition the author discusses how to choose and apply suitable
mathematical tools to several disciplines including pure and applied mathematics physics
engineering neural science material science climate and atmosphere ocean science and many
others. Readers will not only learn detailed techniques for stochastic modeling and prediction
but will develop their intuition as well. Important topics in modeling and prediction including
extreme events high-dimensional systems and multiscale features are discussed.
