Koc, BirgulRubino, SamueleChacón Rebollo, TomásIliescu, Traian2025-07-212025-07-212025-06-04Koc, B., Rubino, S., Chacón Rebollo, T. y Iliescu, T. (2025). Residual-based data-driven variational multiscale reduced order models for parameter-dependent problems. Computational and Applied Mathematics, 44, 308-1. https://doi.org/https://doi.org/10.1007/s40314-025-03273-0.0101-82051807-0302https://hdl.handle.net/11441/175471In 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.application/pdf28 p.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Reduced order modelsVariational multiscaleData-driven modelingResidualinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/s40314-025-03273-0