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One promising direction for addressing this challenge is the use of tensor decompositions, which have proven to be a useful tool for the compact representation of large, high\u2010dimensional data. However, their integration into time\u2010dependent interactive visualization pipelines remains limited. We introduce TT4D, a memory\u2010 and time\u2010efficient lossy compression and decompression technique for four\u2010dimensional (4D) time\u2010varying volume data based on the tensor train (TT) decomposition. Our approach employs efficient subsampling during decomposition to reduce memory consumption and computational cost, enabling the processing of large datasets while avoiding unnecessarily large intermediate matrices and tensors. Beyond compression, TT4D provides a GPU\u2010based, on\u2010the\u2010fly decoding scheme that avoids reconstructing the entire 4D volume, supporting interactive visualization. At equivalent error levels, TT4D outperforms other transform\u2010based compressors at random\u2010access decompression across datasets up to 64GB. Exploiting the structure of TT cores, our approach enables adaptive multiresolution rendering, fast spatio\u2010temporal data exploration, and interactive filtering. Together, these capabilities make TT4D a scalable solution for interactive visualization of high\u2010resolution, time\u2010varying volume data.<\/jats:p>","DOI":"10.1111\/cgf.70471","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T11:09:15Z","timestamp":1781176155000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["TT4D: Tensor\u2010Train\u2010based 4D Time\u2010Dependent Volume Rendering"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-0851-4203","authenticated-orcid":false,"given":"Clara","family":"Hartmann","sequence":"first","affiliation":[{"name":"University of Zurich Department of Informatics  Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5831-2056","authenticated-orcid":false,"given":"Rafael","family":"Ballester\u2010Ripoll","sequence":"additional","affiliation":[{"name":"IE University  Madrid Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6724-526X","authenticated-orcid":false,"given":"Renato","family":"Pajarola","sequence":"additional","affiliation":[{"name":"University of Zurich Department of Informatics  Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,6,11]]},"reference":[{"key":"e_1_2_8_2_2","doi-asserted-by":"crossref","unstructured":"AustinW. 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