Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling

• URL: http://arxiv.org/abs/2205.12419v1
• Date: Wed, 25 May 2022 00:07:57 GMT
• Title: Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling
• Authors: Shady E. Ahmed, Omer San, Adil Rasheed, Traian Iliescu, Alessandro Veneziani
• Abstract summary: We propose a new physics guided machine learning (PGML) paradigm to increase the accuracy of reduced order models (ROMs) at a modest computational cost. The hierarchical structure of the ROM basis and the variational multiscale (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.
• Score: 58.720142291102135
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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