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We propose a new adaptive strategy for linear ROM that allows the reduced mapping to vary dynamically in response to the evolving deformation state, significantly improving accuracy over traditional linear approaches. To further handle large deformations, we introduce a historical displacement basis combined with Grassmann interpolation, enabling the system to recover robustly even in challenging scenarios. We evaluate our method through quantitative online\u2010error analysis and qualitative comparisons with principal component analysis (PCA)\u2010based linear ROM simulations, demonstrating substantial accuracy gains while preserving comparable computational costs.<\/jats:p>","DOI":"10.1111\/cgf.70371","type":"journal-article","created":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T12:40:28Z","timestamp":1774874428000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Interpolated Adaptive Linear Reduced Order Modeling for Deformation Dynamics"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1664-5886","authenticated-orcid":false,"given":"Y.","family":"Tao","sequence":"first","affiliation":[{"name":"University of Wisconsin\u2010Madison  USA"},{"name":"Meta  USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2529-3159","authenticated-orcid":false,"given":"M.","family":"Chiaramonte","sequence":"additional","affiliation":[{"name":"Meta  USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Fernandez","sequence":"additional","affiliation":[{"name":"Meta  USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,3,30]]},"reference":[{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.2514\/1.35374"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/100813051"},{"key":"e_1_2_8_4_2","doi-asserted-by":"crossref","unstructured":"Aigerman Noam Gupta Kunal Kim Vladimir G et al. \u201cNeural jacobian fields: Learning intrinsic mappings of arbitrary meshes\u201d.arXiv preprint arXiv:2205.02904(2022) 3.","DOI":"10.1145\/3528223.3530141"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201387"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073300"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12832"},{"key":"e_1_2_8_8_2","unstructured":"Benchekroun Otman Zhang Jiayi Eris Chaudhuri Siddhartha et al. \u201cFast complementary dynamics via skinning eigen-modes\u201d.arXiv preprint arXiv:2303.11886(2023) 2."},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.111908"},{"key":"e_1_2_8_10_2","doi-asserted-by":"crossref","unstructured":"Chang Yue Chen Peter Yichen Wang Zhecheng et al. \u201cLicrom: Linear-subspace continuous reduced order modeling with neural fields\u201d.SIGGRAPH Asia 2023 Conference Papers.2023 1\u2013123 8.","DOI":"10.1145\/3610548.3618158"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2005.13"},{"key":"e_1_2_8_12_2","unstructured":"Chen Peter Yichen Xiang Jinxu Cho Dong Heon et al. \u201cCROM: Continuous reduced-order modeling of PDEs using implicit neural representations\u201d.arXiv preprint arXiv:2206.02607(2022) 2\u20134."},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/3568952"},{"key":"e_1_2_8_14_2","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964968"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13645"},{"key":"e_1_2_8_16_2","doi-asserted-by":"crossref","unstructured":"Holden Daniel Duong Bang Chi Datta Sayantan andNowrouzezahrai Derek. \u201cSubspace neural physics: Fast data-driven interactive simulation\u201d.Proceedings of the 18th annual ACM SIGGRAPH\/Eurographics Symposium on Computer Animation.2019 1\u2013123.","DOI":"10.1145\/3309486.3340245"},{"key":"e_1_2_8_17_2","unstructured":"Hauser Kris K Shen Chen andO'Brien James F.\u201cInteractive deformation using modal analysis with constraints\u201d. 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