论文标题
物理学指导的机器学习，用于跨尺度降低订单建模的机器学习
Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling
论文作者
论文摘要
我们提出了一个新的物理学指导机器学习（PGML）范式，该范式利用了变异多尺度（VMS）框架和可用数据以适度的计算成本大大提高降低订单模型（ROM）的准确性。 ROM基础和VMS框架的层次结构可以自然地分离已解决的未解决的ROM空间尺度。现代PGML算法用于构建新型模型，以在已解决和未解决的ROM量表之间相互作用。具体而言，新框架构建了最接近VMS框架中真正交互项的ROM运算符。最后，机器学习用于减少投影误差并进一步提高ROM的准确性。我们针对二维涡度传输问题的数值实验表明，新型的PGML-VMS-ROM范式保持了当前ROM的计算成本较低，同时显着提高了ROM的准确性。
We propose a new physics guided machine learning (PGML) paradigm that leverages the variational multiscale (VMS) framework and available data to dramatically increase the accuracy of reduced order models (ROMs) at a modest computational cost. The hierarchical structure of the ROM basis and the VMS framework enable a natural separation of the resolved and unresolved ROM spatial scales. Modern PGML algorithms are used to construct novel models for the interaction among the resolved and unresolved ROM scales. Specifically, the new framework builds ROM operators that are closest to the true interaction terms in the VMS framework. Finally, machine learning is used to reduce the projection error and further increase the ROM accuracy. Our numerical experiments for a two-dimensional vorticity transport problem show that the novel PGML-VMS-ROM paradigm maintains the low computational cost of current ROMs, while significantly increasing the ROM accuracy.
