Chapter 20: A Deep Learning Approach to Improving Reduced Order Models

Meneghetti, Laura; Shah, Nirav N.; Girfoglio, Michele; Demo, Nicola; Tezzele, Marco; Lario, Andrea; Stabile, Giovanni; Rozza, Gianluigi

doi:10.1137/1.9781611977257.ch20

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“…The framework aims then to exploit the capability of POD models for linear prediction, adding the nonlinear term through the DeepONet, which can be viewed as a data-driven closure model. See [57] for another data-driven modelling approach to close ROMs, while for other recent works that propose nonlinear model order reduction, we cite [58][59][60][61][62][63][64].…”

Section: Introductionmentioning

confidence: 99%

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

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Rozza

2023

Adv. Model. and Simul. in Eng. Sci.

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In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the original model. The error introduced by the such operation is usually neglected and sacrificed in order to reach a fast computation. We propose to couple the model reduction to a machine learning residual learning, such that the above-mentioned error can be learned by a neural network and inferred for new predictions. We emphasize that the framework maximizes the exploitation of high-fidelity information, using it for building the reduced order model and for learning the residual. In this work, we explore the integration of proper orthogonal decomposition (POD), and gappy POD for sensors data, with the recent DeepONet architecture. Numerical investigations for a parametric benchmark function and a nonlinear parametric Navier-Stokes problem are presented.

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