Data-Driven Model Order Reduction with pyMOR

2026-07-29

AI Summary

This work addresses the limitations of traditional model-based reduced-order modeling in scenarios where high-fidelity model code is difficult to integrate, necessitating data-driven alternatives. It presents the first systematic integration of data-driven techniques—such as Dynamic Mode Decomposition—with model-driven approaches within the open-source library pyMOR. Built upon a unified interface of VectorArray, Operator, and Model abstractions, the proposed framework enables a flexible and efficient hierarchical reduction pipeline. The study demonstrates seamless interoperability between data-driven and model-driven methods, validates the efficacy of data-driven reduction through practical case studies, and highlights its performance advantages and complementary potential relative to conventional approaches.

Abstract

pyMOR is a free and open-source software library of model order reduction algorithms for the Python programming language. Designed with classical model-based reduction methods for large-scale parametric partial differential equation problems in mind, algorithms in pyMOR are implemented in terms of operations on abstract VectorArray, Operator and Model interfaces, allowing for a seamless integration with external solver codes implementing the full-order model. For cases where a tight integration with the full-order model code is not feasible, data-driven model order reduction algorithms, which only require simulation or measurement data of the full-order model, are an attractive alternative. In this work we discuss the data-driven methods that have been recently added to pyMOR, show practical examples of their application using pyMOR and compare their performance with classical model-based methods. We show that pyMOR serves as a unified framework for combining model-based and data-driven methods, enabling the construction of flexible and efficient hierarchical model reduction pipelines.

Problem

• model order reduction
• data-driven
• full-order model
• parametric partial differential equations
• pyMOR

Innovation

• data-driven model order reduction
• pyMOR
• model-based reduction
• hierarchical model reduction pipelines
• open-source software