Tutorials

• Learning how to create observables
  • Identity
  • Polynomial
  • Time-delays
  • Random Fourier Features
  • Custom observables
  • Concate observables
• Learning how to compute time derivatives
  • Differentiation methods
  • Derivative package
  • Custom differentiation method
• Dynamic mode decomposition on two mixed spatial signals
• Dynamic mode decomposition with control on a 2D linear system
• Dynamic mode decomposition with control (DMDc) for a 128D system
  • Import torus example from the pyKoopman package.
  • Applying DMD
  • Applying DMD with control
  • Compare the eigenvalues of DMD and DMDc with the true eigenvalues.
• Dynamic mode decomposition with control on a high-dimensional linear system
• Successful examples of using Dynamic mode decomposition on PDE system
  • 1. Viscous Burgers equation
  • 2. nonlinear schrodinger equation
  • 3. Revisiting cubic-quintic Ginzburg-Landau equation
• Unsuccessful examples of using Dynamic mode decomposition on PDE system
  • 1. cubic-quintic Ginzburg-Landau equation
  • 2. K-S equation
• Extended DMD for Van Der Pol System
  • Collect training data
  • Koopman regression using EDMD
  • Prediction
  • Visualize
• Learning Koopman eigenfunctions on Slow manifold
  • Collect training data
  • Try EDMD with polynomial features on training data
  • Try NNDMD on training data
  • Try NNDMD on training data but now we enforce the \(A\) to be disspative
  • Check the continuous eigenvalues
  • Evaluate model performance on test trajectory
  • Evaluate linearity of identified Koopman eigenfunctions
  • Observation
• Comparing DMD and KDMD for Slow manifold dynamics
  • 1. Applying DMD
  • 2. Applying KDMD
  • Validate Koopman eigenfunction with an unseen trajectory
  • Validate the learned Koopman eigenfunction
• Extended DMD with control for chaotic duffing oscillator
• Extended DMD with control for Van der Pol oscillator
  • Compare prediction accuracy of Koopman model on a test trajectory
• Hankel Alternative View of Koopman Operator for Lorenz System
  • HAVOK regression
  • Extract forcing signal
  • Prediction using the HAVOK model
• Hankel DMD with control for Van der Pol Oscillator
  • Compare prediction accuracy of Koopman model on a test trajectory
  • Predict using Koopman model
  • Compare results
• Neural Network DMD on Slow Manifold
  • Ways to use NNDMD
• EDMD and NNDMD for a simple linear system
  • Analytic Koopman eigenvalues and eigenfunctions
  • Data-driven approximation with EDMD and polynomial basis functions
  • Data-driven approximation with NN-DMD
  • Check shape of matrices related to Koopman operator
• Sparisfying a minimal Koopman invariant subspace from EDMD for a simple linear system

Useful links

• PyKoopman @ PyPI
• Issue Tracker