Residual-based data-driven variational multiscale reduced order models for parameter-dependent problems
Birgul Koc, Samuele Rubino, Tomás Chacón Rebollo, Traian Iliescu · Computational and Applied Mathematics · 2025
Abstract 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 ( $$\varepsilon = 1e-4$$ ε = 1 e - 4 ); and (iii) a two-dimensional flow past a cylinder at Reynolds number $$Re=1000$$ R e = 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.