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.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.

He pretends to have no talent for cultivating, but in fact already has super strong force. Others think he has no talent, laugh at him, bully him, but he doesn't care, because he has more important things to do.In order to seek the whereabouts of his parents, to regain the prestige of the family, and to protect the safety of the people, he needs to hide his strength and win eventually when others are inadvertent.☆About the Author☆Nan Chen, a new online novel writer, wrote a novel named Greatest Conceited Emperor on the literary website and received high marks. The rich storyline and distinctive character of the book attracted readers.