J. Nathan Kutz - Böcker

Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material - including lecture videos per section, homeworks, data, and code in MATLAB®, Python, Julia, and R - available on databookuw.com.

Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data is an accessible introductory-to-advanced textbook focusing on integrating scientific computing methods and algorithms with modern data analysis techniques, including basic applications of machine learning in the sciences and engineering. Its overarching goal is to develop techniques that allow for the integration of the dynamics of complex systems and big data.This comprehensive textbook provides a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation, data-driven modelling, and machine learning. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological, and physical sciences. The high-level programming language python is used throughout the book to implement and develop mathematical solution strategies. One specific aim of the book is to integrate standard scientific computing methods with the burgeoning field of data analysis, machine learning and Artificial Intelligence (AI). This area of research is expanding at an incredible pace in the sciences due to the proliferation of data collection in almost every field of science. The enormous data sets routinely encountered in the sciences now certainly give a big incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret, and give meaning to the data in the context of its scientific setting. This brings together, in a self-consistent fashion, the key ideas from (i) statistics, (ii) time-frequency analysis and (iii) low-dimensional reductions in order to provide meaningful insight into the data sets one is faced with in any scientific field today, including those generated from complex dynamic systems. This is a tremendously exciting area and much of this part of the book is driven by intuitive examples of how the three areas (i)-(iii) can be used in combination to give critical insight into the fundamental workings of various problems.

Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data is an accessible introductory-to-advanced textbook focusing on integrating scientific computing methods and algorithms with modern data analysis techniques, including basic applications of machine learning in the sciences and engineering. Its overarching goal is to develop techniques that allow for the integration of the dynamics of complex systems and big data.This comprehensive textbook provides a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation, data-driven modelling, and machine learning. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological, and physical sciences. The high-level programming language python is used throughout the book to implement and develop mathematical solution strategies. One specific aim of the book is to integrate standard scientific computing methods with the burgeoning field of data analysis, machine learning and Artificial Intelligence (AI). This area of research is expanding at an incredible pace in the sciences due to the proliferation of data collection in almost every field of science. The enormous data sets routinely encountered in the sciences now certainly give a big incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret, and give meaning to the data in the context of its scientific setting. This brings together, in a self-consistent fashion, the key ideas from (i) statistics, (ii) time-frequency analysis and (iii) low-dimensional reductions in order to provide meaningful insight into the data sets one is faced with in any scientific field today, including those generated from complex dynamic systems. This is a tremendously exciting area and much of this part of the book is driven by intuitive examples of how the three areas (i)-(iii) can be used in combination to give critical insight into the fundamental workings of various problems.

The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from:· statistics,· time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems.Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from:· statistics,· time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems.Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

Data-driven dynamical systems is a burgeoning field, connecting how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is the first book to address the DMD algorithm and present a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development. By blending theoretical development, example codes, and applications, the theory and its many innovations and uses are showcased. The efficacy of the DMD algorithm is shown through the inclusion of example problems from engineering, physical sciences, and biological sciences, and the authors provide extensive MATLAB® code, data for intuitive examples of key methods, and graphical presentations. This book can therefore be used in courses that integrate data analysis with dynamical systems, and will be a useful resource for engineers and applied mathematicians.

This book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields.Consisting of  four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models.The book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate/doctoral classes.