Data-driven modeling & scientific computation : methods for complex systems & big data / J. Nathan Kutz, Department of Applied Mathematics, University of Washington.

Format:

Book

Author/Creator:

Kutz, Jose Nathan, author.

Language:

English

Subjects (All):

MATLAB.

Science--Data processing.

Science.

Numerical analysis.

Differential equations.

Physical Description:

1 online resource

Other Title:

Methods for complex systems & big data

Place of Publication:

Oxford : Oxford University Press, [2026]

Summary:

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.

Contents:

Prolegomenon to modern computing

Basic computations and visualization

Python introduction

Linear systems

Numerical differentiation and integration

Curve fitting

Basic optimization

Advanced curve fitting and machine learning

Visualization

Differential and partial differential equations

Initial and boundary value problems of differential equations

Finite difference methods

Time- and space-stepping schemes: Method of lines

Spectral methods

Finite element methods

Computational methods for data analysis

Statistical methods and their applications

Time-frequency analysis: Fourier transforms and wavelets

Matrix decompositions

Independent component analysis

Unsupervised machine learning

Supervised machine learning

Reinforcement learning

Spatio-temporal data and dynamics

Data assimilation methods

Transformers and foundation models.

Notes:

Includes bibliographical references and index.

Description based upon online resource; title from PDF title page (Oxford Academic, viewed September 15, 2026)

Other Format:

Print version: Kutz, Jose Nathan. Data-driven modeling & scientific computation.

ISBN:

9780198929109

0198929102

OCLC:

1593799427

Access Restriction:

Restricted for use by site license