# Modellreduktion

• pyMOR: Modellreduktion mit Python
• emgr: Modellreduktion von Input-Output Systemen

# Modellreduktion

## $\color{#00568a}{\large{\text{py}}}\color{#e88e3f}{\large{\text{MOR}}}$

pyMOR - Model Order Reduction with Python - is a software library for building model order reduction applications with the Python programming language. Its main focus lies on the application of reduced basis methods to parameterized partial differential equations. All algorithms in pyMOR are formulated in terms of abstract interfaces for seamless integration with external high-dimensional PDE solvers. Moreover, pure Python implementations of finite element and finite volume discretizations using the NumPy/SciPy scientific computing stack are provided for getting started quickly.

Mehr Informationen finden SIe auf der offizielle Homepage.

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• ## emgr

- the Empirical Gramian framework for model reduction of input-output systems. Empirical gramians can be computed for linear and nonlinear state-space control systems for purposes of model order reduction (MOR), system identification (SYSID) and uncertainty quantification (UQ). Model reduction using empirical gramians can be applied to the state-space, to the parameter-space or both through combined reduction. For state reduction, balanced truncation of the empirical controllability gramian and the empirical observability gramian, or alternatively, direct truncation (approximate balancing) of the empirical cross gramian (or the empirical linear cross gramian for large-scale linear systems) is available. For parameter reduction, parameter identification and sensitivity analysis the empirical sensitivity gramian (controllability of parameters) or the empirical identifiability gramian (observability of parameters) are provided. Combined state and parameter reduction is enabled by the empirical joint gramian, which computes controllability and observability of states (cross gramian) and observability of parameters (cross-identifiability gramian) concurrently. The empirical gramian framework - emgr is a compact open-source toolbox for (empirical) GRAMIAN-based model reduction and compatible with OCTAVE and MATLAB. emgr provides a common interface for the computation of empirical gramians and empirical covariance matrices.

Mehr Informationen finden SIe auf der offizielle Homepage.

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