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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 (<jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon = 1e-4$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b5<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mi>e<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>); and (iii) a two-dimensional flow past a cylinder at Reynolds number <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$Re=1000$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>R<\/mml:mi>\n                    <mml:mi>e<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>1000<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. 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.<\/jats:p>","DOI":"10.1007\/s40314-025-03273-0","type":"journal-article","created":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T20:36:43Z","timestamp":1748983003000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Residual-based data-driven variational multiscale reduced order models for parameter-dependent problems"],"prefix":"10.1007","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1733-4862","authenticated-orcid":false,"given":"Birgul","family":"Koc","sequence":"first","affiliation":[]},{"given":"Samuele","family":"Rubino","sequence":"additional","affiliation":[]},{"given":"Tom\u00e1s","family":"Chac\u00f3n Rebollo","sequence":"additional","affiliation":[]},{"given":"Traian","family":"Iliescu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,4]]},"reference":[{"issue":"1","key":"3273_CR1","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/s11831-015-9161-0","volume":"24","author":"N Ahmed","year":"2017","unstructured":"Ahmed N, Chac\u00f3n Rebollo T, John V, Rubino S (2017) A review of variational multiscale methods for the simulation of turbulent incompressible flows. 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