pyMOR - Model Order Reduction with Python

pyMOR is a software library for building model order reduction applications with the Python programming language. Implemented algorithms include reduced basis methods for parametric linear and non-linear problems, as well as system-theoretic methods such as balanced truncation or IRKA. All algorithms in pyMOR are formulated in terms of abstract interfaces for seamless integration with external PDE solver packages. Moreover, pure Python implementations of finite element and finite volume discretizations using the NumPy/SciPy scientific computing stack are provided for getting started quickly.

• Getting started
  • Trying it out
  • The thermalblock demo explained
  • Learning more
• Technical Overview
  • Three Central Classes
  • Base Classes
  • Creating Models
  • Parameters
  • Defaults
  • RuleTables
  • The Reduction Process
• Environment Variables
• pyMOR 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: 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
  • 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
    • Optimizing with the ROM using finite differences
    • Computing the gradient of the objective functional
    • Optimizing using a gradient in FOM
    • Optimizing using a gradient in ROM
    • Beyond the traditional offline/online splitting: enrich along the path of optimization
    • Adaptively enriching along the path
    • Conclusion and some general words about MOR methods for optimization
  • 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
• Release Notes
  • pyMOR 2022.2 (December 18, 2022)
    • Release highlights
      • Eigensystem Realization Algorithm
      • Parametric AAA algorithm
      • Long short-term memory neural networks
      • Time domain analysis of LTIModels
    • Additional new features
      • New approach to handling randomness in pyMOR
      • DWR reductor for output estimation with primal-dual approach
      • Adaptive frequency domain analysis
      • LTIModel can compute LQG and BR Gramians
      • Caching of the dense LU decomposition for NumpyMatrixOperator
    • Further notable improvements
  • pyMOR 2022.1 (July 21, 2022)
    • Release highlights
      • Support for discrete-time systems
      • Structure-preserving model reduction for symplectic systems
    • Additional new features
      • Lots of new features for the neural network based reductors
      • Randomized linear algebra algorithms
      • FEniCS discretizer
      • Simplified VectorArray implementation
    • Backward incompatible changes
      • Dropped Python 3.7 support
    • Further notable improvements
  • pyMOR 2021.2 (December 22, 2021)
    • Release highlights
      • Data-driven model order reduction with Dynamic Mode Decomposition
      • Formalization of Model inputs
    • Additional new features
      • Basic RB output error estimates
      • Experimental scikit-fem support
      • Wachspress’ shifts
    • Backward incompatible changes
      • Transfer function restructuring
    • Further notable improvements
  • pyMOR 2021.1 (September 24, 2021)
    • Release highlights
      • Methods for unstable LTI systems
      • Modal truncation
      • Time-dependent parameter values
    • Additional new features
      • Symbolic ExpressionFunctions
      • Output reductor using ANNs
      • Improvements to the HAPOD algorithm
      • Improved support for Empirical Interpolation of functions
      • Methods for exporting matrices of system models
      • pyMOR is now a pure Python package
    • Backward incompatible changes
      • Drop python 3.6 support
      • Symbolic ExpressionFunctions
    • Further notable improvements
  • pyMOR 2020.2 (December 10, 2020)
    • Release highlights
      • Parameter derivatives of solutions and outputs
      • Neural network reductor for non-stationary problems
      • New tutorials
    • Additional new features
      • Bode plot for input-output systems
      • Iterable VectorArrays
      • Expansion of ConcatenationOperators and improved projection algorithms
      • Support for Python 3.9
    • Backward incompatible changes
      • Updated Model interface
      • Changes in methods for inner products and norms of VectorArrays
      • Restructuring of grid classes
      • Renaming of some Operators
      • Minimal pip and Manylinux wheel version
    • Further notable improvements
  • pyMOR 2020.1 (July 23, 2020)
    • Release highlights
      • Model order reduction using artificial neural networks
      • New system analysis and linear algebra algorithms
      • Improved parameter handling
      • pyMOR tutorial collection
    • Additional new features
      • Improvements to ParameterFunctionals
      • Extended Newton algorithm
      • initial_guess parameter for apply_inverse
      • manylinux 2010+2014 wheels
      • Debugging improvements
      • WebGL-based visualizations
    • Backward incompatible changes
      • Renamed interface classes
      • Module cleanup
      • State ids removed and caching simplified
      • Further API changes
    • Further notable improvements
  • pyMOR 2019.2 (December 16, 2019)
    • Release highlights
      • Implement new models and reductors more easily
      • Extended VectorArray interface with generic complex number support
      • Improved and extended support for system-theoretic MOR methods
      • Model outputs and parameter sensitivities
    • Additional new features
      • Extended FEniCS bindings
      • Improved greedy algorithms
      • Numerical linear algebra algorithms
      • Support for low-rank operators
      • Improved string representations of pyMOR objects
      • Easier working with immutable objects
      • project and assemble_lincomb are easier to extend
      • Improvements to pyMOR’s discretization toolbox
    • Backward incompatible changes
      • Dropped Python 3.5 support
      • Global RandomState
      • Space id handling
      • Further API Changes
    • Further notable improvements
  • pyMOR 0.5 (January 17, 2019)
    • Release highlights
      • Python 3 support
      • System-theoretic MOR methods
      • NGSolve support
      • New linear algebra algorithms
      • VectorArray improvements
      • RuleTable based algorithms
    • Additional new features
    • Backward incompatible changes
    • Further notable improvements
  • pyMOR 0.4 (September 28, 2016)
    • Release highlights
      • FEniCS and deal.II support
      • Parallelization of pyMOR’s reduction algorithms
      • Support classes for MPI distributed external PDE solvers
      • New reduction algorithms
      • Copy-on-write semantics for VectorArrays
      • Improvements to pyMOR’s discretizaion tookit
      • Caching improvements
    • Additional new features
    • Backward incompatible changes
    • Further improvements
  • pyMOR 0.3 (March 2, 2015)
• Bibliography
• Developer Documentation
  • Setting up an Environment for pyMOR Development
    • Getting the source
    • Environment with Virtualenv
    • Environment with docker-compose
  • Coding guidelines and project management
    • Code style
      • How to check code style
    • GitHub project
    • pre-commit hooks
  • pyMOR’s dependencies
  • The Makefile
    • the .env file
  • Continuous Testing / Integration Setup
    • Gitlab CI
      • Stage: Sanity
      • Stage: Test
      • Stage: Build
      • Stage: Install_checks
      • Stage: Deploy
      • Github - Gitlab bridge
    • GitHub Actions
    • Docker images

API Documentation

• API Reference
  • pymor
    • Subpackages
      • algorithms
        • Submodules
      • analyticalproblems
        • Submodules
      • bindings
        • Submodules
      • core
        • Submodules
      • discretizers
        • Subpackages
      • models
        • Submodules
      • operators
        • Submodules
      • parallel
        • Submodules
      • parameters
        • Submodules
      • reductors
        • Submodules
      • scripts
        • Submodules
      • tools
        • Subpackages
        • Submodules
      • vectorarrays
        • Submodules
    • Submodules
      • basic
      • version
        • Module Contents
    • Package Contents
      • filename
      • revstring
      • quit_event_loop
• pymor
  • Subpackages
    • algorithms
      • Submodules
        • adaptivegreedy
        • basic
        • bernoulli
        • dmd
        • ei
        • eigs
        • error
        • genericsolvers
        • gram_schmidt
        • greedy
        • hapod
        • image
        • krylov
        • lincomb
        • line_search
        • lradi
        • lrradi
        • lyapunov
        • newton
        • pod
        • preassemble
        • projection
        • rand_la
        • riccati
        • rules
        • samdp
        • simplify
        • svd_va
        • sylvester
        • symplectic
        • timestepping
        • to_matrix
    • analyticalproblems
      • Submodules
        • burgers
        • domaindescriptions
        • elliptic
        • expressions
        • functions
        • helmholtz
        • instationary
        • text
        • thermalblock
    • bindings
      • Submodules
        • dunegdt
        • fenics
        • ngsolve
        • pymess
        • scipy
        • slycot
    • core
      • Submodules
        • base
        • cache
        • config
        • defaults
        • exceptions
        • logger
        • pickle
    • discretizers
      • Subpackages
        • builtin
        • fenics
        • skfem
    • models
      • Submodules
        • basic
        • interface
        • iosys
        • mpi
        • neural_network
        • symplectic
        • transfer_function
        • transforms
    • operators
      • Submodules
        • block
        • constructions
        • ei
        • interface
        • list
        • mpi
        • numpy
        • symplectic
    • parallel
      • Submodules
        • basic
        • default
        • dummy
        • interface
        • ipython
        • manager
        • mpi
    • parameters
      • Submodules
        • base
        • functionals
    • reductors
      • Submodules
        • aaa
        • basic
        • bt
        • coercive
        • dwr
        • era
        • h2
        • interpolation
        • mt
        • neural_network
        • parabolic
        • residual
        • sobt
        • sor_irka
        • symplectic
    • scripts
      • Submodules
        • pymor_demo
        • pymor_vis
    • tools
      • Subpackages
        • io
      • Submodules
        • context
        • counter
        • deprecated
        • floatcmp
        • formatrepr
        • formatsrc
        • frozendict
        • mpi
        • plot
        • pprint
        • random
        • table
        • timing
        • typer
    • vectorarrays
      • Submodules
        • block
        • constructions
        • interface
        • list
        • mpi
        • numpy
  • Submodules
    • basic
    • version
      • Module Contents
        • HANDLERS
        • LONG_VERSION_PY
        • NotThisMethod
        • VersioneerConfig
        • get_config
        • get_keywords
        • get_versions
        • git_get_keywords
        • git_pieces_from_vcs
        • git_versions_from_keywords
        • plus_or_dot
        • register_vcs_handler
        • render
        • render_git_describe
        • render_git_describe_long
        • render_pep440
        • render_pep440_old
        • render_pep440_post
        • render_pep440_pre
        • run_command
        • versions_from_parentdir
  • Package Contents
    • filename
    • revstring
    • quit_event_loop