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An Efficient, Memory-Saving Approach for the Loewner Framework
The Loewner framework is one of the most successful data-driven model order reduction techniques. If N is the cardinality of a given data set, the so-called Loewner and shifted Loewner matrices [Formula: see text] and [Formula: see text] can be defined by solely relying on information encoded in the...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8924745/ https://www.ncbi.nlm.nih.gov/pubmed/35310540 http://dx.doi.org/10.1007/s10915-022-01800-3 |
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author | Palitta, Davide Lefteriu, Sanda |
author_facet | Palitta, Davide Lefteriu, Sanda |
author_sort | Palitta, Davide |
collection | PubMed |
description | The Loewner framework is one of the most successful data-driven model order reduction techniques. If N is the cardinality of a given data set, the so-called Loewner and shifted Loewner matrices [Formula: see text] and [Formula: see text] can be defined by solely relying on information encoded in the considered data set and they play a crucial role in the computation of the sought rational model approximation.In particular, the singular value decomposition of a linear combination of [Formula: see text] and [Formula: see text] provides the tools needed to construct accurate models which fulfill important approximation properties with respect to the original data set. However, for highly-sampled data sets, the dense nature of [Formula: see text] and [Formula: see text] leads to numerical difficulties, namely the failure to allocate these matrices in certain memory-limited environments or excessive computational costs. Even though they do not possess any sparsity pattern, the Loewner and shifted Loewner matrices are extremely structured and, in this paper, we show how to fully exploit their Cauchy-like structure to reduce the cost of computing accurate rational models while avoiding the explicit allocation of [Formula: see text] and [Formula: see text] . In particular, the use of the hierarchically semiseparable format allows us to remarkably lower both the computational cost and the memory requirements of the Loewner framework obtaining a novel scheme whose costs scale with [Formula: see text] . |
format | Online Article Text |
id | pubmed-8924745 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-89247452022-03-16 An Efficient, Memory-Saving Approach for the Loewner Framework Palitta, Davide Lefteriu, Sanda J Sci Comput Article The Loewner framework is one of the most successful data-driven model order reduction techniques. If N is the cardinality of a given data set, the so-called Loewner and shifted Loewner matrices [Formula: see text] and [Formula: see text] can be defined by solely relying on information encoded in the considered data set and they play a crucial role in the computation of the sought rational model approximation.In particular, the singular value decomposition of a linear combination of [Formula: see text] and [Formula: see text] provides the tools needed to construct accurate models which fulfill important approximation properties with respect to the original data set. However, for highly-sampled data sets, the dense nature of [Formula: see text] and [Formula: see text] leads to numerical difficulties, namely the failure to allocate these matrices in certain memory-limited environments or excessive computational costs. Even though they do not possess any sparsity pattern, the Loewner and shifted Loewner matrices are extremely structured and, in this paper, we show how to fully exploit their Cauchy-like structure to reduce the cost of computing accurate rational models while avoiding the explicit allocation of [Formula: see text] and [Formula: see text] . In particular, the use of the hierarchically semiseparable format allows us to remarkably lower both the computational cost and the memory requirements of the Loewner framework obtaining a novel scheme whose costs scale with [Formula: see text] . Springer US 2022-03-16 2022 /pmc/articles/PMC8924745/ /pubmed/35310540 http://dx.doi.org/10.1007/s10915-022-01800-3 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Palitta, Davide Lefteriu, Sanda An Efficient, Memory-Saving Approach for the Loewner Framework |
title | An Efficient, Memory-Saving Approach for the Loewner Framework |
title_full | An Efficient, Memory-Saving Approach for the Loewner Framework |
title_fullStr | An Efficient, Memory-Saving Approach for the Loewner Framework |
title_full_unstemmed | An Efficient, Memory-Saving Approach for the Loewner Framework |
title_short | An Efficient, Memory-Saving Approach for the Loewner Framework |
title_sort | efficient, memory-saving approach for the loewner framework |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8924745/ https://www.ncbi.nlm.nih.gov/pubmed/35310540 http://dx.doi.org/10.1007/s10915-022-01800-3 |
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