ABSTRACT This paper investigates the recently introduced data-driven correction reduced order model (DDC-ROM) in the numerical simulation of the quasi-geostrophic equations. The DDC-ROM uses available data to model the correction term that is generally used to represent the missing information in low-dimensional ROMs. Physical constraints are added to the DDC-ROM to create the constrained data-driven correction reduced order model (CDDC-ROM) in order to further improve its accuracy and stability. Finally, the DDC-ROM and CDDC-ROM are tested on time intervals that are longer than the time interval over which they were trained. The numerical investigation shows that, for low-dimensional ROMs, both the DDC-ROM and CDDC-ROM perform better than the standard Galerkin ROM (G-ROM) and the CDDC-ROM provides the best results.

中文翻译：

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准地转方程的数据驱动修正降阶模型：数值研究

摘要 本文研究了最近在准地转方程数值模拟中引入的数据驱动校正降阶模型（DDC-ROM）。DDC-ROM 使用可用数据对通常用于表示低维 ROM 中缺失信息的校正项进行建模。在 DDC-ROM 中添加物理约束以创建约束数据驱动的校正降阶模型（CDDC-ROM），以进一步提高其准确性和稳定性。最后，DDC-ROM 和 CDDC-ROM 的测试时间间隔比它们被训练的时间间隔要长。数值研究表明，对于低维 ROM，DDC-ROM 和 CDDC-ROM 的性能都优于标准 Galerkin ROM (G-ROM)，而 CDDC-ROM 的效果最好。