Residual-based data-driven variational multiscale reduced order models for parameter-dependent problems
In this paper, we propose a novel residual-based data-driven closure strategy for reduced order models (ROMs) of under-resolved, convection-dominated problems. The new ROM closure model is constructed in a variational multiscale (VMS) framework by using the available full order model data and a mode...
| Authors: | , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/175471 |
| Online Access: | https://hdl.handle.net/11441/175471 https://doi.org/10.1007/s40314-025-03273-0 |
| Access Level: | Open access |
| Keyword: | Reduced order models Variational multiscale Data-driven modeling Residual |
| Summary: | In this paper, we propose a novel residual-based data-driven closure strategy for reduced order models (ROMs) of under-resolved, convection-dominated problems. The new ROM closure model is constructed in a variational multiscale (VMS) framework by using the available full order model data and a model form ansatz that depends on the ROM residual. We emphasize that this closure modeling strategy is fundamentally different from the current data-driven ROM closures, which generally depend on the ROM coefficients. We investigate the new residual-based data-driven VMS ROM closure strategy in the numerical simulation of three test problems: (i) a one-dimensional parameter-dependent advection-diffusion problem; (ii) a two-dimensional time-dependent advection-diffusion-reaction problem with a small diffusion coefficient (ε=1e−4); and (iii) a two-dimensional flow past a cylinder at Reynolds number Re=1000. Our numerical investigation shows that the new residual-based data-driven VMS-ROM is more accurate than the standard coefficient-based data-driven VMS-ROM. |
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