Multifidelity computing for coupling full and reduced order models

Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and comprise a multifidelity problem sharing an interface between various formulations or heterogeneous computational entities. To this end, we present a robust hybrid analysis and modeling approach combining a physics-based full order model (FOM) and a data-driven reduced order model (ROM) to form the building blocks of an integrated approach among mixed fidelity descriptions toward predictive digital twin technologies. At the interface, we introduce a long short-term memory network to bridge these high and low-fidelity models in various forms of interfacial error correction or prolongation. The proposed interface learning approaches are tested as a new way to address ROM-FOM coupling problems solving nonlinear advection-diffusion flow situations with a bifidelity setup that captures the essence of a broad class of transport processes.

The proposed multifidelity concepts toward hybrid ROM/FOM coupling can be seen below. Dashed blocks refer to the interface learning approaches introduced in the present work: (a) Direct Prolongation Interface (DPI), (b) Prolongation followed by a machine learning Correction Interface (PCI), (c) machine learning Correction followed by a Prolongation Interface (CPI), and (d) Uplifted Prolongation Interface (UPI) where the latent space is enhanced through machine learning before we apply the prolongation operator.

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