Data-Driven Science and Engineering

Singular Value Decomposition (SVD): Overview.
Singular Value Decomposition (SVD): Mathematical Overview.
Singular Value Decomposition (SVD): Matrix Approximation.
Singular Value Decomposition (SVD): Dominant Correlations.
SVD: Image Compression [Matlab].
SVD: Image Compression [Python].
The Frobenius Norm for Matrices.
SVD Method of Snapshots.
Matrix Completion and the Netflix Prize.
Unitary Transformations.
Unitary Transformations and the SVD [Matlab].
Unitary Transformations and the SVD [Python].
Linear Systems of Equations, Least Squares Regression, Pseudoinverse.
Least Squares Regression and the SVD.
Linear Systems of Equations.
Linear Regression.
Linear Regression 1 [Matlab].
Linear Regression 2 [Matlab].
Linear Regression 1 [Python].
Linear Regression 2 [Python].
Linear Regression 3 [Python].
Principal Component Analysis (PCA).
Principal Component Analysis (PCA) [Matlab].
Principal Component Analysis (PCA) 1 [Python].
Principal Component Analysis (PCA) 2 [Python].
SVD: Eigenfaces 1 [Matlab].
SVD: Eigenfaces 2 [Matlab].
SVD: Eigenfaces 3 [Matlab].
SVD: Eigenfaces 4 [Matlab].
SVD: Eigen Action Heros [Matlab].
SVD: Eigenfaces 1 [Python].
SVD: Eigenfaces 2 [Python].
SVD: Eigenfaces 3 [Python].
SVD and Optimal Truncation.
SVD: Optimal Truncation [Matlab].
SVD: Optimal Truncation [Python].
SVD and Alignment: A Cautionary Tale.
SVD: Importance of Alignment [Matlab].
SVD: Importance of Alignment [Python].
Randomized Singular Value Decomposition (SVD).
Randomized SVD: Power Iterations and Oversampling.
Randomized SVD Code [Matlab].
Randomized SVD Code [Python].
Fourier Analysis: Overview.
Fourier Series: Part 1.
Fourier Series: Part 2.
Inner Products in Hilbert Space.
Complex Fourier Series.
Fourier Series [Matlab].
Fourier Series [Python].
Fourier Series and Gibbs Phenomena [Matlab].
Fourier Series and Gibbs Phenomena [Python].
The Fourier Transform.
The Fourier Transform and Derivatives.
The Fourier Transform and Convolution Integrals.
Parseval's Theorem.
Solving the Heat Equation with the Fourier Transform.
The Discrete Fourier Transform (DFT).
Computing the DFT Matrix.
The Fast Fourier Transform (FFT).
The Fast Fourier Transform Algorithm.
Denoising Data with FFT [Matlab].
Denoising Data with FFT [Python].
Computing Derivatives with FFT [Matlab].
Computing Derivatives with FFT [Python].
Solving PDEs with the FFT [Matlab].
Solving PDEs with the FFT [Python].
Solving PDEs with the FFT, Part 2 [Matlab].
Solving PDEs with the FFT, Part 2 [Python].
The Spectrogram and the Gabor Transform.
Spectrogram Examples [Matlab].
Spectrogram Examples [Python].
Uncertainty Principles and the Fourier Transform.
Wavelets and Multiresolution Analysis.
Image Compression and the FFT.
Image Compression with Wavelets (Examples in Python).
Image Compression with the FFT (Examples in Matlab).
Image Compression and Wavelets (Examples in Matlab).
Image Compression and the FFT (Examples in Python).
The Laplace Transform: A Generalized Fourier Transform.
Laplace Transforms and Differential Equations.
Laplace Transform Examples.
Sparsity and Compression: An Overview.
Data-driven Modeling of Traveling Waves.
Machine Learning for Fluid Mechanics.
Data-Driven Resolvent Analysis.
Data-driven nonlinear aeroelastic models of morphing wings for control.
Model Predictive Control.
Robust Principal Component Analysis (RPCA).
Deep Learning of Hierarchical Multiscale Differential Equation Time Steppers.
Reinforcement Learning: Machine Learning Meets Control Theory.
Deep Reinforcement Learning: Neural Networks for Learning Control Laws.
Deep Reinforcement Learning for Fluid Dynamics and Control.
Overview of Deep Reinforcement Learning Methods.
Reinforcement Learning Series: Overview of Methods.
Model Based Reinforcement Learning: Policy Iteration, Value Iteration, and Dynamic Programming.
Q-Learning: Model Free Reinforcement Learning and Temporal Difference Learning.
Nonlinear Control: Hamilton Jacobi Bellman (HJB) and Dynamic Programming.