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  • pyMOR -- Generic Algorithms and Interfaces for Model Order Reduction

    SIAM Journal on Scientific ComputingVol. 38, No. 5, pp. S194–S2162016

    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.

  • A New Certified Hierarchical and Adaptive RB-ML-ROM Surrogate Model for Parametrized PDEs

    SIAM Journal on Scientific ComputingVol. 45, No. 3, pp. A1039–A10652023

    Abstract

    We present a new surrogate modeling technique for efficient approximation of input-output maps governed by parametrized PDEs. The model is hierarchical as it is built on a full order model, reduced order model (ROM), and machine learning (ML) model chain. The model is adaptive in the sense that the ROM and ML model are adapted on the fly during a sequence of parametric requests to the model. To allow for a certification of the model hierarchy, as well as to control the adaptation process, we employ rigorous a posteriori error estimates for the ROM and ML models. In particular, we provide an example of an ML-based model that allows for rigorous analytical quality statements. We demonstrate the efficiency of the modeling chain on a Monte Carlo and a parameter-optimization example. Here, the ROM is instantiated by Reduced Basis methods, and the ML model is given by a neural network or by a kernel model using vectorial kernel orthogonal greedy algorithms.