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You can find the video lectures on YouTube.

The associated Julia code (in the form of Jupyter Notebooks) can be found in the "notebooks" folder. In case a certain package is missing in your Julia version, you can simply add a cell before the first one containing the two code lines
using Pkg
Pkg.add("name_of_package")

References to related literature can be found at the end of this Readme file.

• Week 1:

  • Solution of scalar linear autonomous ODEs (DS4DS 1.01)
  • Solution of vectorial linear autonomous ODEs (DS4DS 1.02)
  • Matrix exponential solution via diagonalization (DS4DS 1.03)
  • Spring-mass-damper as an autonomous state-space system example (DS4DS 1.04)
  • State stability of autonomous state-space systems (DS4DS 1.05)
  • Nonlinear ODEs (1.06)

• Week 2:

  • Numerical solutions of ODEs 1 (DS4DS 1.07)
  • Numerical solutions of ODEs 2 (DS4DS 1.08)
  • Numerical solutions of ODEs 3 (DS4DS 1.09)
  • State-space models with inputs (DS4DS 1.10)
  • Exact solution of linear state-space models (DS4DS 1.11)
  • Observability 1 (DS4DS 1.12)
  • Observability 2 (DS4DS 1.13)
  • Observability 3 (DS4DS 1.14)
  • Discrete dynamical systems (DS4DS 1.15)

• Week 3:

  • Partial differential equations: Introduction (DS4DS 1.16)
  • Partial differential equations: Derivation of the heat equation (DS4DS 1.17)
  • Partial differential equations: Spatial discretization (DS4DS 1.18)
  • Partial differential equations: Discretization in space and time (DS4DS 1.19)

• Week 4:

  • Linear model identification: intro part 1/2 (DS4DS 2.01)
  • Linear model identification: intro part 2/2 (DS4DS 2.02)
  • Linear least squares solution (DS4DS 2.03)
  • Ordinary least squares: static example (DS4DS 2.04)
  • Ordinary least squares: bias (DS4DS 2.05)
  • Ordinary least squares: covariance (DS4DS 2.06)
  • Ordinary least squares: consistency (DS4DS 2.07)

• Week 5:

  • Multicollinearity (DS4DS 2.08)
  • Ridge regression (DS4DS 2.09)
  • Weighted least squares: motivation & solution (DS4DS 2.10)
  • Weighted least squares: example (DS4DS 2.11)
  • Recursive least squares: derivation part 1/2 (DS4DS 2.12)
  • Recursive least squares: derivation part 2/2 (DS4DS 2.13)
  • Recursive least squares: exponential forgetting (DS4DS 2.14)
  • Recursive least squares: example (DS4DS 2.15)

• Week 6:

  • Ordinary Least Squares for Dynamical Systems: Introduction (DS4DS 2.16)
  • Ordinary Least Squares for Dynamical Systems: Example (DS4DS 2.17)
  • Ordinary Least Squares for Dynamical Systems: Limitations (DS4DS 2.18)
  • Singular Value Decomposition: Motivation (DS4DS 2.19)
  • Singular Value Decomposition: Interpretation (DS4DS 2.20)
  • Eigendecomposition of continuous and discrete-time dynamical systems (DS4DS 2.21)
  • Dynamic Mode Decomposition: Concept (DS4DS 2.22)
  • Dynamic Mode Decomposition: Efficient computation (DS4DS 2.23)

• Week 7:

  • Training nonlinear models (DS4DS 3.01)
  • The hypothesis space (DS4DS 3.02)
  • Gradient descent 1 (DS4DS 3.03)
  • Gradient descent 2 (DS4DS 3.04)
  • Gradient descent 3 (DS4DS 3.05)
  • Gradient descent 4 (DS4DS 3.06)
  • The Armijo and Wolfe conditions (DS4DS 3.07)
  • Stochastic gradient descent (DS4DS 3.08)

• Week 8:

  • Momentum (DS4DS 3.09)
  • Convergence rates (DS4DS 3.10)
  • Newton's method (DS4DS 3.11)
  • Differentiation Techniques: Overview (DS4DS 3.12)
  • Symbolic Differentiation (DS4DS 3.13)
  • Algorithmic Differentiation: Forward mode (DS4DS 3.14)
  • Algorithmic Differentiation: Backward mode (DS4DS 3.15)

• Week 9:

  • Constrained optimization 1 (DS4DS 3.16)
  • Constrained optimization 2 (DS4DS 3.17)
  • Constrained optimization 3 (DS4DS 3.18)
  • Penalty methods and Sequential Quadratic Programming (DS4DS 3.19)
  • The active set method 1 (DS4DS 3.20)
  • The active set method 2 (DS4DS 3.21)

• Week 10:

  • Optimization-based parameter identification (DS4DS 4.01)
  • Impact of the prediction horizon in data-driven modeling (DS4DS 4.02)
  • Nonlinear prediction error method identification (DS4DS 4.03)
  • Global vs. local optima in nonlinear data-driven modeling (DS4DS 4.04)
  • Identification of an unknown initial state (DS4DS 4.05)
  • Utilizing constrained optimization for incorporating a priori knowledge (DS4DS 4.06)

• Week 11:

  • Neural ordinary differential equations - NODEs (DS4DS 4.07)
  • Sampled input data for NODE modeling (DS4DS 4.08)
  • Hammerstein-Wiener models in NODEs (DS4DS 4.09)
  • Extrapolation of data-driven dynamical models (DS4DS 4.10)
  • Discrete-time nonlinear system identification (DS4DS 4.11)

• Week 12:
  • Feature Engineering - Introduction (DS4DS 5.01)
  • Manual feature selection using dictionaries (DS4DS 5.02)
  • Extracting linear features from data (DS4DS 5.03)
  • Feature engineering using autoencoders (DS4DS 5.04)
  • The role of features in deep learning (DS4DS 5.05)

• Week 13:
  • Overfitting and the bias-variance tradeoff (DS4DS 6.01)
  • Cross validation (DS4DS 6.02)
  • Sparsity and the L1 norm (DS4DS 6.03)
  • Subdifferentials of non-differentiable functions (DS4DS 6.04)
  • The LASSO algorithm for model selection (DS4DS 6.05)
  • Sparse identification of nonlinear dynamics (SINDy) (DS4DS 6.06)

• Week 14:
  • Optimal control - Introduction (DS4DS 7.01)
  • Optimal control in discrete time (DS4DS 7.02)
  • Optimal control of linear systems 1 - Dynamics (DS4DS 7.03)
  • Optimal control of linear systems 2 - Objective function (DS4DS 7.04)
  • Optimal control of linear systems 3 - Example (DS4DS 7.05)
  • Linear model predictive control (DS4DS 7.06)
  • Data-driven model predictive control using DMD (DS4DS 7.07)
  • Differential predictive control: introduction (DS4DS 7.08)
  • Differential predictive control: global vs. local optima (DS4DS 7.09)

• An introduction to the Koopman Operator (DS4DS 8.01)
• Koopman operator: Spectral decomposition 1 (DS4DS 8.02)
• Koopman operator: Spectral decomposition 2 (DS4DS 8.03)
• Koopman: Observable functions (DS4DS 8.04)
• Extended Dynamic Mode Decomposition 1 - Finite dimensional subspaces (DS4DS 8.05)
• Extended Dynamic Mode Decomposition 2 - The EDMD algorithm (DS4DS 8.06)
• Extended Dynamic Mode Decomposition 3 - Koopman eigenfunctions (DS4DS 8.07)
• Extended Dynamic Mode Decomposition 4 - Koopman modes & Summary (DS4DS 8.08)
• Dynamic Mode Decomposition as a special case of EDMD (DS4DS 8.09)
• kernel EDMD 1 - Motivation & kernel trick (DS4DS 8.10)
• kernel EDMD 2 - Main algorithm (DS4DS 8.11)
• kernel EDMD 3 - Koopman eigenfunctions and modes (DS4DS 8.12)
• The Koopman Generator (DS4DS 8.13)
• Extended DMD for the Koopman Generator (DS4DS 8.14)

• Data science and machine learning:

  • Y. S. Abu-Mostafa, M. Magdon-Ismail and H.-T. Lin. "Learning from data: A short course." AMLBook, 2012. (URL)
  • S. L. Brunton and J. N. Kutz. "Data-Driven Science and Engineering." Cambridge University Press, 2019. (DOI)
  • C. M. Bishop. "Pattern Recognition and Machine Learning." Springer, 2007. (URL)

• Dynamical systems and system identification:

  • R. Isermann and M. Münchhof. "Identification of Dynamic Systems." Springer, 2011. (DOI)
  • O. Nelles. "Nonlinear System Identification." Springer, 2001. (DOI)

• Optimization

  • G. Nocedal and S. J. Wright. "Numerical Optimization." (DOI)
  • The book by Nelles also has an extensive introduction to optimization.