Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling
This work addresses the challenge of enhancing ROM accuracy for computational fluid dynamics applications, representing an incremental improvement by combining existing frameworks with machine learning.
The authors tackled the problem of improving the accuracy of reduced order models (ROMs) without increasing computational cost by proposing a physics guided machine learning paradigm that integrates the variational multiscale framework and data-driven techniques, achieving significant accuracy gains in numerical experiments for a two-dimensional vorticity transport problem.
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.