Tutorials

• Tutorial: Using pyMOR’s discretization toolkit
  • A first equation without parameters
  • Defining boundary conditions
  • Another example
  • Data functions defined from pixel graphics
  • A parametric problem
  • Multiple parameters
  • Parameter-separability
• Tutorial: Building a Reduced Basis
  • Model setup
  • Computing the snapshot data
  • A trivial reduced basis
  • Strong greedy algorithm
  • Orthonormalization required
  • Proper Orthogonal Decomposition
  • Weak greedy algorithm
• Tutorial: Projecting a Model
  • Model setup
  • Solving the Model
  • Galerkin Projection
  • Building the ROM
  • Offline/Online Decomposition
  • Letting pyMOR do the work
  • Using Reductors
• Tutorial: Linear time-invariant systems
  • Building a model
  • Time-domain simulation
  • Transfer function evaluation
  • Magnitude and Bode plots
  • System poles
  • System Gramians
  • Hankel singular values
  • System norms
• Tutorial: Reducing an LTI system using balanced truncation
  • Balanced truncation
  • Balanced truncation in pyMOR
• Tutorial: Interpolatory model order reduction for LTI systems
  • Interpolation at infinity
  • Interpolation at zero
  • Interpolation at an arbitrary finite point
  • Interpolation at multiple points
• Tutorial: Model order reduction for port-Hamiltonian systems
  • Port-Hamiltonian LTI systems
  • A toy problem: Mass-spring-damper chain
  • Structure-preserving model order reduction
    • pH-IRKA
    • Positive-real balanced truncation (PRBT)
    • Passivity preserving model reduction via spectral factorization
    • Comparison
• Tutorial: Model order reduction for unstable LTI systems
  • An unstable model
  • Frequency domain balanced truncation
  • Gap-IRKA
• Tutorial: Model order reduction with artificial neural networks
  • Feedforward neural networks
  • A non-intrusive reduced order method using artificial neural networks
  • Direct approximation of output quantities
  • Neural networks for instationary problems
    • Long short-term memory neural networks for instationary problems
      • The architecture of an LSTM neural network
      • The LSTM cell
        • The forget gate
        • The input gate
        • The output gate
      • LSTMs for model order reduction
    • Instationary neural network reductors in practice
• Tutorial: Model order reduction for PDE-constrained optimization problems
  • An elliptic model problem with a linear objective functional
  • Optimizing with the FOM using finite differences
  • Computing the gradient of the objective functional
  • Optimizing using a gradient in FOM
  • Adaptive trust-region optimization using reduced basis methods
  • Conclusion and some general words about MOR methods for optimization
• Tutorial: Exploring Models interactively in a jupyter environment
• Tutorial: VectorArray Basics
  • What are VectorArrays and what are they used for in pyMOR?
  • VectorSpaces / How to create VectorArrays
  • Converting NumPy arrays to VectorArrays
  • Converting VectorArrays to NumPy arrays
  • Rows and columns
  • Basic operations
  • Copies
  • Indexing and views
  • DOF access
  • Complex Numbers
  • VectorSpace ids
  • Internals / other types of arrays
• Tutorial: Binding an external PDE solver to pyMOR
  • Defining the PDE solver
  • Binding the solver to Python
  • Using the exported Python classes with pyMOR
  • Putting it all together