Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder
| dc.contributor.author | Cooper, Rachel | en |
| dc.contributor.author | Popov, Andrey A. | en |
| dc.contributor.author | Sandu, Adrian | en |
| dc.date.accessioned | 2022-02-27T04:03:52Z | en |
| dc.date.available | 2022-02-27T04:03:52Z | en |
| dc.date.issued | 2021-08-27 | en |
| dc.date.updated | 2022-02-27T04:03:51Z | en |
| dc.description.abstract | Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of freedom. Traditional ROM techniques such as proper orthogonal decomposition (POD) focus on linear projections of the dynamics onto a set of spectral features. In this paper we explore the construction of ROM using autoencoders (AE) that perform nonlinear projections of the system dynamics onto a low dimensional manifold learned from data. The approach uses convolutional neural networks (CNN) to learn spatial features as opposed to spectral, and utilize a physics informed (PI) cost function in order to capture temporal features as well. Our investigation using the quasi-geostrophic equations reveals that while the PI cost function helps with spatial reconstruction, spatial features are less powerful than spectral features, and that construction of ROMs through machine learning-based methods requires significant investigation into novel non-standard methodologies. | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.orcid | Sandu, Adrian [0000-0002-5380-0103] | en |
| dc.identifier.uri | http://hdl.handle.net/10919/108894 | en |
| dc.language.iso | en | en |
| dc.relation.uri | http://arxiv.org/abs/2108.12344v1 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | cs.LG | en |
| dc.title | Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder | en |
| dc.type | Article | en |
| dc.type.dcmitype | Text | en |
| pubs.organisational-group | /Virginia Tech | en |
| pubs.organisational-group | /Virginia Tech/Engineering | en |
| pubs.organisational-group | /Virginia Tech/Engineering/Computer Science | en |
| pubs.organisational-group | /Virginia Tech/All T&R Faculty | en |
| pubs.organisational-group | /Virginia Tech/Engineering/COE T&R Faculty | en |
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