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<p>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 (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3273_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="76" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon = 1e-4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>=</mo> <mn>1</mn> <mi>e</mi> <mo>-</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>); and (iii) a two-dimensional flow past a cylinder at Reynolds number <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3273_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="76" /> </InlineMediaObject> <EquationSource Format="TEX">\(Re=1000\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>1000</mn> </mrow> </math></EquationSource> </InlineEquation>. 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.</p>

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Residual-based data-driven variational multiscale reduced order models for parameter-dependent problems

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  • 出版模式：

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  • 发表日期：

    2025年6月4日

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  • Birgul Koc,
  • Samuele Rubino,
  • Tomás Chacón Rebollo,
  • Traian Iliescu

摘要

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.