AI 中文总结
scikit-rom是基于scikit-fem的开源Python库，提供透明可修改的基于投影的ROM流程，含四种超降阶策略及示例，适用于ROM领域教学、研讨与研究原型设计。
AI 中文摘要
基于投影的降阶模型（ROM）已成为加速参数密集型工程模拟的核心技术，但该方法的教学和原型设计仍颇具挑战。其难点在于多阶段工作流程，包括快照生成、SVD/POD基构造、Galerkin投影、离线-在线分解、超降阶及误差评估。现有软件框架要么将这些阶段封装在高级接口后，要么依赖编译的整体求解器栈，学生和早期研究人员难以检查或修改。本文介绍scikit-rom，这是一个开源Python库，旨在使完整的基于投影的ROM流程透明、可修改，适合基于交互式笔记本的探索。该库构建于轻量级有限元后端scikit-fem之上，提供模块化问题模板及专用工具，用于快照生成、降阶基构造、降阶算子组装、在线ROM求解、超降阶和定量精度评估，所有功能整合在统一流程中。超降阶支持四种策略：离散经验插值方法（DEIM）、S-OPT采样、能量守恒采样与加权（ECSW）方案及ECM型求积构造。四个递进式示例引导读者从全阶模拟到ROM及超降阶模型的构造，涵盖线性、非线性、静态和瞬态问题类别。该库适用于降阶模型社区的研究生教学、密集型研讨会及研究原型设计。源代码和示例可在该http URL获取，文档可在该http URL获取。
英文摘要
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.
