PyMOR: Difference between revisions

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Synopsis

pyMOR is a BSD-licensed software library for building model order reduction applications in 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 and iterative rational Krylov algorithm. pyMOR is designed from the ground up for easy integration with external PDE solver packages but also offers Python-based discretizations for getting started easily.

Features

Currently, the following model reduction algorithms are provided by pyMOR:

A generic reduction routine for projection of arbitrary high-dimensional discretizations onto reduced spaces, preserving (possibly nested) affine decompositions of operators and functionals for efficient offline/online decomposition.
Efficient error estimation for linear affinely decomposed problems.
Empirical interpolation of arbitrary operators (with efficient evaluation of projected interpolated operators if the operator supports restriction to selected degrees of freedom).
Parallel adaptive greedy and POD algorithms for reduced space construction.
Empirical-Interpolation-Greedy and DEIM algorithms for generation of interpolation data for empirical operator interpolation.
Balanced-based and interpolation-based reduction methods for first-order and second-order linear time-invariant systems.
Model order reduction using artificial neural networks.
Data-driven model order reduction with Dynamic Mode Decomposition, Eigensystem Realization, parametric AAA.
Gram-Schmidt algorithm supporting re-orthogonalization for improved numerical accuracy.
Time-stepping and Newton algorithms, as well as generic iterative linear solvers.
Low-rank alternating direction implicit (LR ADI) method for large-scale Lyapunov equations and bindings for matric equations solvers in SLICOT (via slycot) and Py-M.E.S.S.
Eigenvalue/pole computation using the implicitly restarted Arnoldi method and the subspace accelerated dominant pole (SAMDP) algorithm.
Modal truncation for linear time-invariant systems.
Time-dependent parameters.

All these algorithms are formulated in terms of abstract interfaces for seamless integration with external high-dimensional PDE solvers. Bindings for the following PDE solver libraries are available:

deal.II
DUNE
FEniCS
NGSolve
scikit-fem (experimental)

Pure Python implementations of discretizations using the NumPy/SciPy scientific computing stack are implemented to provide an easy-to-use sandbox for experimentation with new model reduction approaches. pyMOR offers:

Structured 1D and 2D grids, as well as an experimental Gmsh-based grid, implementing the same abstract grid interface.
Finite element and finite volume operators based on this interface.
SciPy/SuperLU based iterative and direct solvers for sparse systems.
OpenGL and matplotlib based visualizations of solutions.

References

M. Ohlberger, S. Rave, S. Schmidt, S. Zhang. "A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries". Springer Proceedings in Mathematics & Statistics Vol. 78: Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, Berlin, June 2014.
R. Milk, S. Rave, F. Schindler. "pyMOR - Generic Algorithms and Interfaces for Model Order Reduction". SIAM Journal on Scientific Computing 38(5): S194--S216, 2016.

Links

Official website,
Development of pyMOR can be tracked on GitHub,
Online documentation.

Contact

For assistance with, and contributions to pyMOR, the developers can be contacted via GitHub discussions.

@@ Line 6: / Line 6: @@
 [https://pymor.org pyMOR] is a [https://opensource.org/licenses/BSD-2-Clause BSD-licensed] software library for building model order reduction applications in the [[:Wikipedia:Python_(programming_language)|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 and iterative rational Krylov algorithm.
-'''pyMOR''' is designed from the ground up for easy integration with external [[List_of_abbreviations#PDE|PDE]] solver packages but also offers Python-based discretizations for getting started easily.
+'''pyMOR''' is designed from the ground up for easy integration with external PDE solver packages but also offers Python-based discretizations for getting started easily.
 == Features ==
@@ Line 14: / Line 14: @@
 * Efficient error estimation for linear affinely decomposed problems.
 * Empirical interpolation of arbitrary operators (with efficient evaluation of projected interpolated operators if the operator supports restriction to selected degrees of freedom).
-* Parallel adaptive greedy and [[List_of_abbreviations#POD|POD]] algorithms for reduced space construction.
+* Parallel adaptive greedy and POD algorithms for reduced space construction.
-* Empirical-Interpolation-Greedy and [[List_of_abbreviations#DEIM|DEIM]] algorithms for generation of interpolation data for empirical operator interpolation.
+* Empirical-Interpolation-Greedy and DEIM algorithms for generation of interpolation data for empirical operator interpolation.
 * Balanced-based and interpolation-based reduction methods for first-order and second-order linear time-invariant systems.
 * Model order reduction using artificial neural networks.
@@ Line 26: / Line 26: @@
 * Time-dependent parameters.
-All these algorithms are formulated in terms of abstract interfaces for seamless integration with external high-dimensional [[List_of_abbreviations#PDE|PDE]] solvers.
+All these algorithms are formulated in terms of abstract interfaces for seamless integration with external high-dimensional PDE solvers.
 Bindings for the following PDE solver libraries are available:
 * [http://www.dealii.org/ deal.II]