PEBL-ROM: Projection-error based local reduced-order models

David Amsallem,Bernard Haasdonk

doi:10.1186/s40323-016-0059-7

Abstract

Projection-based model order reduction (MOR) using local subspaces is becoming an increasingly important topic in the context of the fast simulation of complex nonlinear models. Most approaches rely on multiple local spaces constructed using parameter, time or state-space partitioning. State-space partitioning is usually based on Euclidean distances. This work highlights the fact that the Euclidean distance is suboptimal and that local MOR procedures can be improved by the use of a metric directly related to the projections underlying the reduction. More specifically, scale-invariances of the underlying model can be captured by the use of a true projection error as a dissimilarity criterion instead of the Euclidean distance. The capability of the proposed approach to construct local and compact reduced subspaces is illustrated by approximation experiments of several data sets and by the model reduction of two nonlinear systems.

Highlights

Projection-based model-order reduction (MOR) is an indispensable tool for accelerating large-scale computational procedures and enabling their solutions in real-time
The goal of this paper is to present a framework in order to approximate the data and associated dynamical system by local approximation spaces
A PEBL-reduced order model (ROM) approach for local nonlinear model reduction is presented in this work

Summary

Introduction

Projection-based model-order reduction (MOR) is an indispensable tool for accelerating large-scale computational procedures and enabling their solutions in real-time. This class of approaches proceeds by restricting the solution to a subspace of the entire solution space, resulting in a much smaller set of equations. One can mention the transition from laminar to turbulent flows, bifurcation of solutions and moving features such as shocks and discontinuities. These simulations are difficult to reduce using classical projection-based MOR as they may require the projection onto large subspaces. Local subspaces can be defined in time [1,2], parameter space [4,5,6], solution features [7] or state-space [3,6,8,9,10]

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