Data-Driven Modeling & Scientific Computation Methods for Complex Systems & Big Data

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:
DT statistics,
DT time-frequency analysis, and
DT 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.

J. Nathan Kutz, Professor of Applied Mathematics, University of Washington

Professor Kutz is the Robert Bolles and Yasuko Endo Professor of Applied Mathematics at the University of Washington. Prof. Kutz was awarded the B.S. in physics and mathematics from the University of Washington (Seattle, WA) in 1990 and the PhD in Applied Mathematics from Northwestern University (Evanston, IL) in 1994. He joined the Department of Applied Mathematics, University of Washington in 1998 and became Chair in 2007.

Professor Kutz is especially interested in a unified approach to applied mathematics that includes modeling, computation and analysis. His area of current interest concerns phenomena in complex systems and data analysis (dimensionality reduction, compressive sensing, machine learning), neuroscience (neuro-sensory systems, networks of neurons), and the optical sciences (laser dynamics and modelocking, solitons, pattern formation in nonlinear optics).

I Basic Computations and Visualization
1. MATLAB Introduction
2. Linear Systems
3. Curve Fitting
4. Numerical Differentiation and Integration
5. Basic Optimization
6. Visualization
II Differential and Partial Differential Equations
7. Initial and Boundary Value Problems of Differential Equations144
8. Finite Difference Methods
9. Time and Space Stepping Schemes: Method of Lines
10. Spectral Methods
11. Finite Element Methods
III Computational Methods for Data Analysis
12. Statistical Methods and Their Applications
13. Time-Frequency Analysis: Fourier Transforms and Wavelets
14. Image Processing and Analysis
15. Linear Algebra and Singular Value Decomposition
16. Independent Component Analysis
17. Image Recognition
18. Basics of Compressed Sensing
19. Dimensionality Reduction for Partial Differential Equations
20. Dynamic Mode Decomposition
21. Data Assimilation Methods
22. Equation Free Modeling
IV Scientific Applications
23. Applications of Differential Equations and Boundary Value Problems
24. Quantum Mechanics
25. Applications of Partial Differential Equations
26. Applications of Data Analysis