{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T17:30:00Z","timestamp":1770917400819,"version":"3.50.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T00:00:00Z","timestamp":1683158400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T00:00:00Z","timestamp":1683158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61973270"],"award-info":[{"award-number":["61973270"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Mach Intell"],"DOI":"10.1038\/s42256-023-00648-y","type":"journal-article","created":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T16:02:48Z","timestamp":1683216168000},"page":"505-517","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Recurrent graph optimal transport for learning 3D flow motion in particle tracking"],"prefix":"10.1038","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3026-9126","authenticated-orcid":false,"given":"Jiaming","family":"Liang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2759-6364","authenticated-orcid":false,"given":"Chao","family":"Xu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0122-6864","authenticated-orcid":false,"given":"Shengze","family":"Cai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,4]]},"reference":[{"key":"648_CR1","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1038\/d41586-019-02144-z","volume":"571","author":"M Kemp","year":"2019","unstructured":"Kemp, M. Leonardo da Vinci\u2019s laboratory: studies in flow. Nature 571, 322\u2013324 (2019).","journal-title":"Nature"},{"key":"648_CR2","doi-asserted-by":"crossref","unstructured":"Dabiri, D. & Pecora, C. Particle Tracking Velocimetry (IOP, 2020).","DOI":"10.1088\/978-0-7503-2203-4"},{"key":"648_CR3","doi-asserted-by":"publisher","first-page":"eabi7716","DOI":"10.1126\/sciadv.abi7716","volume":"7","author":"A Kopitca","year":"2021","unstructured":"Kopitca, A., Latifi, K. & Zhou, Q. Programmable assembly of particles on a Chladni plate. Sci. Adv. 7, eabi7716 (2021).","journal-title":"Sci. Adv."},{"key":"648_CR4","doi-asserted-by":"publisher","first-page":"1363","DOI":"10.1038\/s41467-017-01681-3","volume":"8","author":"B Ferdowsi","year":"2017","unstructured":"Ferdowsi, B., Ortiz, C. P., Houssais, M. & Jerolmack, D. J. River-bed armouring as a granular segregation phenomenon. Nat. Commun. 8, 1363 (2017).","journal-title":"Nat. Commun."},{"key":"648_CR5","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1038\/nature01793","volume":"424","author":"DL Hu","year":"2003","unstructured":"Hu, D. L., Chan, B. & Bush, J. W. The hydrodynamics of water strider locomotion. Nature 424, 663\u2013666 (2003).","journal-title":"Nature"},{"key":"648_CR6","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1038\/nature13070","volume":"508","author":"B He","year":"2014","unstructured":"He, B., Doubrovinski, K., Polyakov, O. & Wieschaus, E. Apical constriction drives tissue-scale hydrodynamic flow to mediate cell elongation. Nature 508, 392\u2013396 (2014).","journal-title":"Nature"},{"key":"648_CR7","doi-asserted-by":"publisher","first-page":"eaax7171","DOI":"10.1126\/science.aax7171","volume":"367","author":"H Mestre","year":"2020","unstructured":"Mestre, H. et al. Cerebrospinal fluid influx drives acute ischemic tissue swelling. Science 367, eaax7171 (2020).","journal-title":"Science"},{"key":"648_CR8","first-page":"1","volume":"13","author":"Z Zhang","year":"2022","unstructured":"Zhang, Z., Hwang, M., Kilbaugh, T. J., Sridharan, A. & Katz, J. Cerebral microcirculation mapped by echo particle tracking velocimetry quantifies the intracranial pressure and detects ischemia. Nat. Commun. 13, 1\u201315 (2022).","journal-title":"Nat. Commun."},{"key":"648_CR9","doi-asserted-by":"publisher","first-page":"822","DOI":"10.1016\/j.cell.2014.06.051","volume":"158","author":"M Guo","year":"2014","unstructured":"Guo, M. et al. Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy. Cell 158, 822\u2013832 (2014).","journal-title":"Cell"},{"key":"648_CR10","doi-asserted-by":"publisher","first-page":"eabd1240","DOI":"10.1126\/sciadv.abd1240","volume":"7","author":"Y Peng","year":"2021","unstructured":"Peng, Y., Liu, Z. & Cheng, X. Imaging the emergence of bacterial turbulence: phase diagram and transition kinetics. Sci. Adv. 7, eabd1240 (2021).","journal-title":"Sci. Adv."},{"key":"648_CR11","doi-asserted-by":"publisher","first-page":"eaav4803","DOI":"10.1126\/sciadv.aav4803","volume":"5","author":"S Schuerle","year":"2019","unstructured":"Schuerle, S. et al. Synthetic and living micropropellers for convection-enhanced nanoparticle transport. Sci. Adv. 5, eaav4803 (2019).","journal-title":"Sci. Adv."},{"key":"648_CR12","doi-asserted-by":"publisher","first-page":"658","DOI":"10.1038\/nphys3041","volume":"10","author":"H Punzmann","year":"2014","unstructured":"Punzmann, H., Francois, N., Xia, H., Falkovich, G. & Shats, M. Generation and reversal of surface flows by propagating waves. Nat. Phys. 10, 658\u2013663 (2014).","journal-title":"Nat. Phys."},{"key":"648_CR13","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1126\/science.1242248","volume":"342","author":"PY Huang","year":"2013","unstructured":"Huang, P. Y. et al. Imaging atomic rearrangements in two-dimensional silica glass: watching silica\u2019s dance. Science 342, 224\u2013227 (2013).","journal-title":"Science"},{"key":"648_CR14","doi-asserted-by":"publisher","first-page":"1680","DOI":"10.1088\/0957-0233\/17\/7\/006","volume":"17","author":"F Pereira","year":"2006","unstructured":"Pereira, F., St\u00fcer, H., Graff, E. C. & Gharib, M. Two-frame 3D particle tracking. Meas. Sci. Technol. 17, 1680 (2006).","journal-title":"Meas. Sci. Technol."},{"key":"648_CR15","doi-asserted-by":"publisher","first-page":"5655","DOI":"10.1073\/pnas.1918296117","volume":"117","author":"SE Leggett","year":"2020","unstructured":"Leggett, S. E. et al. Mechanophenotyping of 3D multicellular clusters using displacement arrays of rendered tractions. Proc. Natl Acad. Sci. USA 117, 5655\u20135663 (2020).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"648_CR16","doi-asserted-by":"crossref","unstructured":"Raffel, M. et al. Particle Image Velocimetry: A Practical Guide (Springer, 2018).","DOI":"10.1007\/978-3-319-68852-7"},{"key":"648_CR17","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.1007\/s00348-013-1533-3","volume":"54","author":"C Cierpka","year":"2013","unstructured":"Cierpka, C., L\u00fctke, B. & K\u00e4hler, C. J. Higher order multi-frame particle tracking velocimetry. Exp. Fluids 54, 1533 (2013).","journal-title":"Exp. Fluids"},{"key":"648_CR18","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1146\/annurev-fluid-010719-060214","volume":"52","author":"SL Brunton","year":"2020","unstructured":"Brunton, S. L., Noack, B. R. & Koumoutsakos, P. Machine learning for fluid mechanics. Ann. Rev. Fluid Mech. 52, 477\u2013508 (2020).","journal-title":"Ann. Rev. Fluid Mech."},{"key":"648_CR19","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s00348-019-2717-2","volume":"60","author":"S Cai","year":"2019","unstructured":"Cai, S., Zhou, S., Xu, C. & Gao, Q. Dense motion estimation of particle images via a convolutional neural network. Exp. Fluids 60, 73 (2019).","journal-title":"Exp. Fluids"},{"key":"648_CR20","doi-asserted-by":"publisher","first-page":"3538","DOI":"10.1109\/TIM.2019.2932649","volume":"69","author":"S Cai","year":"2019","unstructured":"Cai, S., Liang, J., Gao, Q., Xu, C. & Wei, R. Particle image velocimetry based on a deep learning motion estimator. IEEE Trans. Instrum. Meas. 69, 3538\u20133554 (2019).","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"648_CR21","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1049\/iet-csr.2019.0040","volume":"2","author":"J Liang","year":"2020","unstructured":"Liang, J., Cai, S., Xu, C. & Chu, J. Filtering enhanced tomographic PIV reconstruction based on deep neural networks. IET Cyber-Syst. Robot. 2, 43\u201352 (2020).","journal-title":"IET Cyber-Syst. Robot."},{"key":"648_CR22","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1038\/s42256-021-00369-0","volume":"3","author":"C Lagemann","year":"2021","unstructured":"Lagemann, C., Lagemann, K., Mukherjee, S. & Schr\u00f6der, W. Deep recurrent optical flow learning for particle image velocimetry data. Nat. Mach. Intell. 3, 641\u2013651 (2021).","journal-title":"Nat. Mach. Intell."},{"key":"648_CR23","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1007\/s00348-019-2861-8","volume":"61","author":"Y Gim","year":"2020","unstructured":"Gim, Y., Jang, D. K., Sohn, D. K., Kim, H. & Ko, H. S. Three-dimensional particle tracking velocimetry using shallow neural network for real-time analysis. Exp. Fluids 61, 26 (2020).","journal-title":"Exp. Fluids"},{"key":"648_CR24","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s00348-020-03061-y","volume":"61","author":"K Mallery","year":"2020","unstructured":"Mallery, K., Shao, S. & Hong, J. Dense particle tracking using a learned predictive model. Exp. Fluids 61, 223 (2020).","journal-title":"Exp. Fluids"},{"key":"648_CR25","unstructured":"Qi, C. R., Su, H., Mo, K. & Guibas, L. J. Pointnet: deep learning on point sets for 3D classification and segmentation. In Proc. IEEE Conference on Computer Vision and Pattern Recognition 652\u2013660 (IEEE, 2017)."},{"key":"648_CR26","doi-asserted-by":"crossref","unstructured":"Liu, X., Qi, C. R. & Guibas, L. J. FlowNet3D: learning scene flow in 3D point clouds. In Proc. IEEE\/CVF Conference on Computer Vision and Pattern Recognition 529\u2013537 (IEEE, CVF, 2019).","DOI":"10.1109\/CVPR.2019.00062"},{"key":"648_CR27","doi-asserted-by":"crossref","unstructured":"Puy, G., Boulch, A. & Marlet, R. FLOT: scene flow on point clouds guided by optimal transport. In European Conference on Computer Vision 527\u2013544 (Springer, 2020).","DOI":"10.1007\/978-3-030-58604-1_32"},{"key":"648_CR28","doi-asserted-by":"crossref","unstructured":"Wu, W., Wang, Z. Y., Li, Z., Liu, W. & Fuxin, L. PointPWC-Net: cost volume on point clouds for (self-) supervised scene flow estimation. In European Conference on Computer Vision 88\u2013107 (Springer, 2020).","DOI":"10.1007\/978-3-030-58558-7_6"},{"key":"648_CR29","doi-asserted-by":"crossref","unstructured":"Wei, Y., Wang, Z., Rao, Y., Lu, J. & Zhou, J. PV-RAFT: point-voxel correlation fields for scene flow estimation of point clouds. In Proc. IEEE\/CVF Conference on Computer Vision and Pattern Recognition 6954\u20136963 (IEEE, CVF, 2021).","DOI":"10.1109\/CVPR46437.2021.00688"},{"key":"648_CR30","first-page":"9594090","volume":"71","author":"J Liang","year":"2021","unstructured":"Liang, J., Cai, S., Xu, C., Chen, T. & Chu, J. DeepPTV: particle tracking velocimetry for complex flow motion via deep neural networks.IEEE Trans. Instrum. Meas. 71, 9594090 (2021).","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"648_CR31","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/TNNLS.2020.2978386","volume":"32","author":"Z Wu","year":"2020","unstructured":"Wu, Z. et al. A comprehensive survey on graph neural networks. IEEE Trans. Neural Netw. Learn. Syst. 32, 4\u201324 (2020).","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"648_CR32","doi-asserted-by":"publisher","first-page":"107725","DOI":"10.1016\/j.dib.2021.107725","volume":"40","author":"AR Khojasteh","year":"2022","unstructured":"Khojasteh, A. R., Laizet, S., Heitz, D. & Yang, Y. Lagrangian and Eulerian dataset of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900. Data Brief 40, 107725 (2022).","journal-title":"Data Brief"},{"key":"648_CR33","doi-asserted-by":"publisher","first-page":"5581","DOI":"10.1038\/s41598-018-23488-y","volume":"8","author":"M Patel","year":"2018","unstructured":"Patel, M., Leggett, S. E., Landauer, A. K., Wong, I. Y. & Franck, C. Rapid, topology-based particle tracking for high-resolution measurements of large complex 3D motion fields. Sci. Rep. 8, 5581 (2018).","journal-title":"Sci. Rep."},{"key":"648_CR34","doi-asserted-by":"publisher","first-page":"101204","DOI":"10.1016\/j.softx.2022.101204","volume":"19","author":"J Yang","year":"2022","unstructured":"Yang, J. et al. SerialTrack: ScalE and rotation invariant augmented Lagrangian particle tracking. SoftwareX 19, 101204 (2022).","journal-title":"SoftwareX"},{"key":"648_CR35","doi-asserted-by":"crossref","unstructured":"Teed, Z. & Deng, J. Raft: Recurrent all-pairs field transforms for optical flow. In European Conference on Computer Vision 402\u2013419 (Springer, 2020).","DOI":"10.1007\/978-3-030-58536-5_24"},{"key":"648_CR36","unstructured":"Sanchez-Gonzalez, A., et al. Learning to simulate complex physics with graph networks. In International Conference on Machine Learning 8459\u20138468 (PMLR, 2020)."},{"key":"648_CR37","unstructured":"Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A. & Battaglia, P. Learning mesh-based simulation with graph networks. In International Conference on Learning Representations 2837 (ICLR, 2021)."},{"key":"648_CR38","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1007\/s00348-016-2157-1","volume":"57","author":"D Schanz","year":"2016","unstructured":"Schanz, D., Gesemann, S. & Schr\u00f6der, A. Shake-The-Box: Lagrangian particle tracking at high particle image densities. Exp. Fluids 57, 70 (2016).","journal-title":"Exp. Fluids"},{"key":"648_CR39","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s00348-019-2875-2","volume":"61","author":"S Tan","year":"2020","unstructured":"Tan, S., Salibindla, A., Masuk, A. U. M. & Ni, R. Introducing OpenLPT: new method of removing ghost particles and high-concentration particle shadow tracking. Exp. Fluids 61, 47 (2020).","journal-title":"Exp. Fluids"},{"key":"648_CR40","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s00348-019-2859-2","volume":"61","author":"P Cornic","year":"2020","unstructured":"Cornic, P. et al. Double-frame tomographic PTV at high seeding densities. Exp. Fluids 61, 23 (2020).","journal-title":"Exp. Fluids"},{"key":"648_CR41","unstructured":"Qi, C. R., Yi, L., Su, H. & Guibas, L. J. PointNet++: deep hierarchical feature learning on point sets in a metric space. In Advances in Neural Information Processing Systems Vol. 30 (NeurIPS, 2017)."},{"key":"648_CR42","first-page":"1","volume":"38","author":"Y Wang","year":"2019","unstructured":"Wang, Y. et al. Dynamic graph CNN for learning on point clouds. ACM Trans. Graphics 38, 1\u201312 (2019).","journal-title":"ACM Trans. Graphics"},{"key":"648_CR43","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1561\/2200000073","volume":"11","author":"G Peyr\u00e9","year":"2019","unstructured":"Peyr\u00e9, G. et al. Computational optimal transport: with applications to data science. Found. Trends Mach. Learn. 11, 355\u2013607 (2019).","journal-title":"Found. Trends Mach. Learn."},{"key":"648_CR44","unstructured":"Cuturi, M. Sinkhorn distances: lightspeed computation of optimal transport. In Advances in Neural Information Processing Systems Vol. 26 (NeurIPS, 2013)."},{"key":"648_CR45","doi-asserted-by":"crossref","unstructured":"Li, Y. et al. A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbulence 9, N31 (2008).","DOI":"10.1080\/14685240802376389"},{"key":"648_CR46","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1002\/fld.1650190502","volume":"19","author":"CR Ethier","year":"1994","unstructured":"Ethier, C. R. & Steinman, D. Exact fully 3D Navier\u2013Stokes solutions for benchmarking. Int. J. Numer. Methods Fluids 19, 369\u2013375 (1994).","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"648_CR47","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/BF00190953","volume":"15","author":"H Maas","year":"1993","unstructured":"Maas, H., Gruen, A. & Papantoniou, D. Particle tracking velocimetry in three-dimensional flows. Exp. Fluids 15, 133\u2013146 (1993).","journal-title":"Exp. Fluids"},{"key":"648_CR48","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s00348-020-03021-6","volume":"61","author":"S Bhattacharya","year":"2020","unstructured":"Bhattacharya, S. & Vlachos, P. P. Volumetric particle tracking velocimetry (PTV) uncertainty quantification. Exp. Fluids 61, 197 (2020).","journal-title":"Exp. Fluids"},{"key":"648_CR49","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/s00348-009-0728-0","volume":"47","author":"C Atkinson","year":"2009","unstructured":"Atkinson, C. & Soria, J. An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp. Fluids 47, 553\u2013568 (2009).","journal-title":"Exp. Fluids"},{"key":"648_CR50","doi-asserted-by":"publisher","first-page":"3042","DOI":"10.1038\/s41596-018-0077-7","volume":"13","author":"MT Scimone","year":"2018","unstructured":"Scimone, M. T. et al. Modular approach for resolving and mapping complex neural and other cellular structures and their associated deformation fields in three dimensions. Nat. Protocols 13, 3042\u20133064 (2018).","journal-title":"Nat. Protocols"}],"container-title":["Nature Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s42256-023-00648-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s42256-023-00648-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s42256-023-00648-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T18:09:59Z","timestamp":1703095799000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s42256-023-00648-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,4]]},"references-count":50,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["648"],"URL":"https:\/\/doi.org\/10.1038\/s42256-023-00648-y","relation":{},"ISSN":["2522-5839"],"issn-type":[{"value":"2522-5839","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,4]]},"assertion":[{"value":"13 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}