Multivariate predictions of local reduced-order-model errors and dimensions
| dc.contributor.author | Moosavi, Azam | en |
| dc.contributor.author | Stefanescu, Razvan | en |
| dc.contributor.author | Sandu, Adrian | en |
| dc.contributor.department | Computer Science | en |
| dc.date.accessioned | 2017-03-06T18:28:21Z | en |
| dc.date.available | 2017-03-06T18:28:21Z | en |
| dc.date.issued | 2017-01-16 | en |
| dc.description.abstract | This paper introduces multivariate input-output models to predict the errors and bases dimensions of local parametric Proper Orthogonal Decomposition reduced-order models. We refer to these multivariate mappings as the MP-LROM models. We employ Gaussian Processes and Artificial Neural Networks to construct approximations of these multivariate mappings. Numerical results with a viscous Burgers model illustrate the performance and potential of the machine learning based regression MP-LROM models to approximate the characteristics of parametric local reduced-order models. The predicted reduced-order models errors are compared against the multi-fidelity correction and reduced order model error surrogates methods predictions, whereas the predicted reduced-order dimensions are tested against the standard method based on the spectrum of snapshots matrix. Since the MP-LROM models incorporate more features and elements to construct the probabilistic mappings they achieve more accurate results. However, for high-dimensional parametric spaces, the MP-LROM models might suffer from the curse of dimensionality. Scalability challenges of MP-LROM models and the feasible ways of addressing them are also discussed in this study. | en |
| dc.description.notes | 19 pages, 15 figures, 7 tables. arXiv admin note: substantial text overlap with arXiv:1511.02909 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/75257 | en |
| dc.language.iso | en | en |
| dc.relation.uri | http://arxiv.org/abs/1701.03720v1 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | cs.NA | en |
| dc.title | Multivariate predictions of local reduced-order-model errors and dimensions | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |
| pubs.organisational-group | /Virginia Tech | en |
| pubs.organisational-group | /Virginia Tech/All T&R Faculty | en |
| pubs.organisational-group | /Virginia Tech/Engineering | en |
| pubs.organisational-group | /Virginia Tech/Engineering/COE T&R Faculty | en |
| pubs.organisational-group | /Virginia Tech/Engineering/Computer Science | en |