pyMOR -- Generic Algorithms and Interfaces for Model Order Reduction

Abstract

Abstract. Reduced basis methods are projection-based model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss the design of pyMOR, a freely available software library of model order reduction algorithms, in particular reduced basis methods, implemented with the Python programming language. As its main design feature, all reduction algorithms in pyMOR are implemented generically via operations on well-defined vector array, operator and discretization interface classes. This allows for an easy integration with existing open-source high-performance partial differential equation solvers without adding any model reduction specific code to these solvers. Besides an in-depth discussion of pyMOR's design philosophy and architecture, we present several benchmark results and numerical examples showing the feasibility of our approach. Key words. model order reduction, reduced basis method, empirical interpolation, scientific computing, software, Python AMS subject classifications. 35-04, 35J20, 35L03, 65-04, 65N30, 65Y05, 68N01.1. Introduction. Over the past years, model order reduction methods have become an important part of many numerical simulation workflows for handling large-scale application problems. Reduced basis (RB) methods are a popular family of such reduction techniques, applicable to parametrized high-dimensional models described by partial differential equations (PDEs). The main ingredient of RB methods is a Galerkin projection of the differential equation onto a problem-adapted reduced subspace generated from solution snapshots of a high-dimensional approximation of the problem for certain wellchosen sampling parameters. While the high-dimensional approximation using standard discretization techniques (such as finite element methods) often yields discrete function spaces with millions of degrees of freedoms, the reduced spaces generated by RB methods typically are of order 100 or smaller, while still retaining the same approximation quality for the problem at hand as the high-dimensional space. In practice, model order reduction by RB approximation can lead to speedups of up to several orders of magnitude. By now, a large body of literature has emerged which theoretically proves and practically demonstrates the applicability of the RB approach to a large variety of application problems (see, e.g., the recent monographs [18,30], the tutorial [15], and the references therein).

EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications

“…In this setup the high-dimensional quantities and all grid structures are implemented in D . The model order reduction as such is implemented in Python using pyMOR [45]. The model reduction algorithms in pyMOR follow a solver agnostic design principle.…”

Mass conservative reduced order modeling of a free boundary osmotic cell swelling problem

“…We introduce some notation for bilinear and linear forms appearing in (14) and (19) which simplify the presentation of the model order reduction approach below: Problem (14) becomes…”

A long short-term memory embedding for hybrid uplifted reduced order models

“…Our results show robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency.Keywords Hybrid analysis and modeling · Supervised machine learning · Long short-term memory · Model reduction · Galerkin projection · Grassmann manifold.Reduced order models (ROMs) have shown great success for prototypical problems in different fields. In particular, Galerkin projection (GP) coupled with proper orthogonal decomposition (POD) capability to extract the most energetic modes has been used to build ROMs for linear and nonlinear systems [22][23][24][25][26][27][28][29]. These ROMs preserve sufficient arXiv:1912.06756v1 [physics.flu-dyn]…”