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A registration method for model order reduction: data compression and geometry reduction
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| dc.contributor.author | TADDEI, Tommaso | |
| dc.date.accessioned | 2024-04-04T02:57:50Z | |
| dc.date.available | 2024-04-04T02:57:50Z | |
| dc.date.created | 2020-01-23 | |
| dc.date.issued | 2020-04-08 | |
| dc.identifier.issn | 1064-8275 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192599 | |
| dc.description.abstractEn | We propose a general---i.e., independent of the underlying equation---registration method for parameterized model order reduction. Given the spatial domain $\Omega \subset \mathbb{R}^d$ and the manifold $\mathcal{M}_{u}= \{ u_{\mu} : \mu \in \mathcal{P} \}$ associated with the parameter domain $\mathcal{P} \subset \mathbb{R}^P$ and the parametric field $\mu \mapsto u_{\mu} \in L^2(\Omega)$, the algorithm takes as input a set of snapshots $\{ u^k \}_{k=1}^{n_{\rm train}} \subset \mathcal{M}_{u}$ and returns a parameter-dependent bijective mapping ${\Phi}: \Omega \times \mathcal{P} \to \mathbb{R}^d$: the mapping is designed to make the mapped manifold $\{ u_{\mu} \circ {\Phi}_{\mu}: \, \mu \in \mathcal{P} \}$ more suited for linear compression methods. We apply the registration procedure, in combination with a linear compression method, to devise low-dimensional representations of solution manifolds with slowly decaying Kolmogorov $N$-widths; we also consider the application to problems in parameterized geometries. We present a theoretical result to show the mathematical rigor of the registration procedure. We further present numerical results for several two-dimensional problems, to empirically demonstrate the effectivity of our proposal. | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.subject.en | Model order reduction | |
| dc.subject.en | Data compression | |
| dc.subject.en | Geometry registration | |
| dc.subject.en | Parameterized partial differential equations | |
| dc.title.en | A registration method for model order reduction: data compression and geometry reduction | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math] | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.identifier.arxiv | 1906.11008 | |
| bordeaux.journal | SIAM Journal on Scientific Computing | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02430234 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02430234v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Scientific%20Computing&rft.date=2020-04-08&rft.eissn=1064-8275&rft.issn=1064-8275&rft.au=TADDEI,%20Tommaso&rft.genre=article |
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