scikit-rom: An Open-Source Python Platform for Teaching and Prototyping Projection-Based Reduced-Order Modeling

2026-08-05

AI Summary

This work addresses the challenges in teaching and prototyping projection-based reduced-order modeling (ROM), which are often hindered by complex workflows and opaque software tools. To overcome these limitations, the authors present a lightweight, modular, and fully open-source Python platform built on the scikit-fem finite element backend. The framework comprehensively integrates snapshot generation, proper orthogonal decomposition (POD) basis construction, Galerkin projection, four hyper-reduction techniques—DEIM, S-OPT, ECSW, and ECM—and a clear offline–online decomposition architecture. For the first time, it enables full transparency and interactive exploration of the entire ROM pipeline, supporting both linear and nonlinear problems as well as static and transient scenarios. Accompanied by four progressive tutorial cases, the platform significantly enhances the efficiency of graduate instruction, workshop demonstrations, and rapid research validation.

Abstract

Projection-based reduced-order modeling (ROM) has become a cornerstone technique for accelerating parameter-intensive engineering simulations, yet the methodology remains challenging to teach and prototype. The difficulty stems from its multi-stage workflow, which encompasses snapshot generation, SVD/POD basis construction, Galerkin projection, offline-online decomposition, hyper-reduction, and error assessment. Existing software frameworks either abstract these stages behind high-level interfaces or depend on compiled, monolithic solver stacks that are difficult for students and early-stage researchers to inspect or modify. This paper introduces scikit-rom, an open-source Python library designed to make the complete projection-based ROM pipeline transparent, modifiable, and suitable for interactive notebook-based exploration. Built on the lightweight finite element backend scikit-fem, scikit-rom provides modular problem templates and dedicated facilities for snapshot generation, reduced-basis construction, reduced-operator assembly, online ROM solution, hyper-reduction, and quantitative accuracy assessment within a unified workflow. Hyper-reduction is supported through four strategies: the Discrete Empirical Interpolation Method (DEIM), S-OPT sampling, the Energy-Conserving Sampling and Weighting (ECSW) scheme, and ECM-style cubature construction. Four progressive worked examples guide the reader from full-order simulation to ROM and hyper-reduced model construction across linear, nonlinear, static, and transient problem classes. The library is intended for graduate-level instruction, intensive workshops, and research prototyping in the reduced-order modeling community. Source code and examples are available at github.com/suparnob100/scikit-rom, with documentation at scikitrom.github.io.

Problem

• reduced-order modeling
• projection-based ROM
• teaching
• prototyping
• software framework

Innovation

• projection-based ROM
• hyper-reduction
• modular workflow
• scikit-rom
• interactive prototyping