AI 中文总结
本研究介绍了pyMOR新增的数据驱动模型降阶方法，对比其与经典基于模型方法的性能，表明pyMOR是整合两类方法的统一框架，可构建灵活高效的分层模型降阶流程。
AI 中文摘要
pyMOR是面向Python编程语言的免费开源模型降阶算法软件库，其设计初衷是针对大规模参数偏微分方程问题的经典基于模型的降阶方法，库中的算法通过对抽象VectorArray、Operator和Model接口的操作实现，可与实现全阶模型的外部求解器代码无缝集成。对于无法与全阶模型代码紧密集成的场景，仅需全阶模型仿真或测量数据的数据驱动模型降阶算法是颇具吸引力的替代方案。本研究讨论了pyMOR近期新增的数据驱动方法，展示了使用pyMOR应用这些方法的实际案例，并将其性能与经典基于模型的方法进行对比。结果表明，pyMOR是整合基于模型与数据驱动方法的统一框架，可构建灵活高效的分层模型降阶流程。
英文摘要
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.
