DATA-DRIVEN MODELING & SCIENTIFIC COMPUTATION METHODS FOR COMPLEX SYSTEMS & BIG DATA2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

DATA-DRIVEN MODELING & SCIENTIFIC COMPUTATION METHODS FOR COMPLEX SYSTEMS & BIG DATAPDF格式电子书版下载

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PART Ⅰ Basic Computations and Visualization3

1 MATLAB Introduction3

1.1 Vectors and Matrices3

1.2 Logic，Loops and Iterations9

1.3 Iteration：The Newton-Raphson Method13

1.4 Function Calls，Input/Output Interactions and Debugging18

1.5 Plotting and Importing/Exporting Data23

2 Linear Systems31

2.1 Direct Solution Methods for Ax = b31

2.2 Iterative Solution Methods for Ax = b35

2.3 Gradient （Steepest） Descent for Ax = b39

2.4 Eigenvalues，Eigenvectors and Solvability44

2.5 Eigenvalues and Eigenvectors for Face Recognition49

2.6 Nonlinear Systems56

3 Curve Fitting61

3.1 Least-Square Fitting Methods61

3.2 Polynomial Fits and Splines65

3.3 Data Fitting with MATLAB69

4 Numerical Differentiation and Integration77

4.1 Numerical Differentiation77

4.2 Numerical Integration83

4.3 Implementation of Differentiation and Integration87

5 Basic Optimization93

5.1 Unconstrained Optimization （Derivative-Free Methods）93

5.2 Unconstrained Optimization （Derivative Methods）99

5.3 Linear Programming105

5.4 Simplex Method110

5.5 Genetic Algorithms113

6 Visualization119

6.1 Customizing Plots and Basic 2D Plotting119

6.2 More 2D and 3D Plotting125

6.3 Movies and Animations131

PART Ⅱ Differential and Partial Differential Equations137

7 Initial and Boundary Value Problems of Differential Equations137

7.1 Initial Value Problems：Euler，Runge-Kutta and Adams Methods137

7.2 Error Analysis for Time-Stepping Routines144

7.3 Advanced Time-Stepping Algorithms149

7.4 Boundary Value Problems：The Shooting Method153

7.5 Implementation of Shooting and Convergence Studies160

7.6 Boundary Value Problems：Direct Solve and Relaxation164

7.7 Implementing MATLAB for Boundary Value Problems167

7.8 Linear Operators and Computing Spectra172

8 Finite Difference Methods180

8.1 Finite Difference Discretization180

8.2 Advanced Iterative Solution Methods for Ax = b186

8.3 Fast Poisson Solvers：The Fourier Transform186

8.4 Comparison of Solution Techniques for Ax = b：Rules of Thumb190

8.5 Overcoming Computational Difficulties195

9 Time and Space Stepping Schemes：Method of Lines200

9.1 Basic Time-Stepping Schemes200

9.2 Time-Stepping Schemes：Explicit and Implicit Methods205

9.3 Stability Analysis209

9.4 Comparison of Time-Stepping Schemes213

9.5 Operator Splitting Techniques216

9.6 Optimizing Computational Performance：Rules of Thumb219

10 Spectral Methods225

10.1 Fast Fourier Transforms and Cosine/Sine Transform225

10.2 Chebychev Polynomials and Transform229

10.3 Spectral Method Implementation233

10.4 Pseudo-Spectral Techniques with Filtering235

10.5 Boundary Conditions and the Chebychev Transform240

10.6 Implementing the Chebychev Transform244

10.7 Computing Spectra：The Floquet-Fourier-Hill Method249

11 Finite Element Methods256

11.1 Finite Element Basis256

11.2 Discretizing with Finite Elements and Boundaries261

11.3 MATLAB for Partial Differential Equations266

11.4 MATLAB Partial Differential Equations Toolbox271

PART Ⅲ Computational Methods for Data Analysis279

12 Statistical Methods and Their Applications279

12.1 Basic Probability Concepts279

12.2 Random Variables and Statistical Concepts286

12.3 Hypothesis Testing and Statistical Significance294

13 Time-Frequency Analysis：Fourier Transforms and Wavelets301

13.1 Basics of Fourier Series and the Fourier Transform301

13.2 FFT Application：Radar Detection and Filtering308

13.3 FFT Application：Radar Detection and Averaging316

13.4 Time-Frequency Analysis：Windowed Fourier Transforms322

13.5 Time-Frequency Analysis and Wavelets328

13.6 Multi-Resolution Analysis and the Wavelet Basis335

13.7 Spectrograms and the Gabor Transform in MATLAB340

13.8 MATLAB Filter Design and Wavelet Toolboxes346

14 Image Processing and Analysis358

14.1 Basic Concepts and Analysis of Images358

14.2 Linear Filtering for Image Denoising364

14.3 Diffusion and Image Processing369

15 Linear Algebra and Singular Value Decomposition376

15.1 Basics of the Singular Value Decomposition （SVD）376

15.2 The SVD in Broader Context381

15.3 Introduction to Principal Component Analysis （PCA）387

15.4 Principal Components，Diagonalization and SVD391

15.5 Principal Components and Proper Orthogonal Modes395

15.6 Robust PCA403

16 Independent Component Analysis412

16.1 The Concept of Independent Components412

16.2 Image Separation Problem419

16.3 Image Separation and MATLAB424

17 Image Recognition：Basics of Machine Learning431

17.1 Recognizing Dogs and Cats431

17.2 The SVD and Linear Discrimination Analysis436

17.3 Implementing Cat/Dog Recognition in MATLAB445

18 Basics of Compressed Sensing449

18.1 Beyond Least-Square Fitting：The L1 Norm449

18.2 Signal Reconstruction and Circumventing Nyquist456

18.3 Data （Image） Reconstruction from Sparse Sampling464

19 Dimensionality Reduction for Partial Differential Equations472

19.1 Modal Expansion Techniques for PDEs472

19.2 PDE Dynamics in the Right （Best） Basis478

19.3 Global Normal Forms of Bifurcation Structures in PDEs482

19.4 The POD Method and Symmetries/Invariances492

19.5 POD Using Robust PCA499

20 Dynamic Mode Decomposition506

20.1 Theory of Dynamic Mode Decomposition （DMD）506

20.2 Dynamics of DMD Versus POD510

20.3 Applications of DMD515

21 Data Assimilation Methods521

21.1 Theory of Data Assimilation521

21.2 Data Assimilation，Sampling and Kalman Filtering526

21.3 Data Assimilation for the Lorenz Equation529

22 Equation-Free Modeling537

22.1 Multi-Scale Physics：An Equation-Free Approach537

22.2 Lifting and Restricting in Equation-Free Computing542

22.3 Equation-Free Space-Time Dynamics547

23 Complex Dynamical Systems：Combining Dimensionality Reduction，Compressive Sensing and Machine Learning551

23.1 Combining Data Methods for Complex Systems551

23.2 Implementing a Dynamical Systems Library556

23.3 Flow Around a Cylinder：A Prototypical Example564

PART Ⅳ Scientific Applications573

24 Applications of Differential Equations and Boundary Value Problems573

24.1 Neuroscience and the Hodgkin-Huxley Model573

24.2 Celestial Mechanics and the Three-Body Problem577

24.3 Atmospheric Motion and the Lorenz Equations581

24.4 Quantum Mechanics585

24.5 Electromagnetic Waveguides588

25 Applications of Partial Differential Equations590

25.1 The Wave Equation590

25.2 Mode-Locked Lasers593

25.3 Bose-Einstein Condensates600

25.4 Advection-Diffusion and Atmospheric Dynamics604

25.5 Introduction to Reaction-Diffusion Systems611

25.6 Steady State Flow Over an Airfoil616

26 Applications of Data Analysis620

26.1 Analyzing Music Scores and the Gabor Transform620

26.2 Image Denoising through Filtering and Diffusion622

26.3 Oscillating Mass and Dimensionality Reduction625

26.4 Music Genre Identification626

References629

Index of MATLAB Commands634

Index636