Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling

TL;DR

This paper introduces a physics-guided machine learning approach integrated with the variational multiscale framework to enhance the accuracy of reduced order models in fluid dynamics, maintaining low computational costs.

Contribution

It develops a novel PGML-VMS-ROM framework that constructs ROM operators aligned with true VMS interactions and reduces projection errors for improved accuracy.

Findings

Significantly increased ROM accuracy in vorticity transport simulations.

Maintained low computational cost comparable to existing ROMs.

Validated effectiveness through numerical experiments.

Abstract

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.