{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T03:37:54Z","timestamp":1777865874407,"version":"3.51.4"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171466"],"award-info":[{"award-number":["12171466"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271025"],"award-info":[{"award-number":["12271025"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["92470119"],"award-info":[{"award-number":["92470119"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2026,4,30]]},"DOI":"10.1137\/24m171499x","type":"journal-article","created":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:36:42Z","timestamp":1777534602000},"page":"537-564","source":"Crossref","is-referenced-by-count":0,"title":["A Deformation-Based Framework for Learning Solution Mappings of PDEs Defined on Varying Domains"],"prefix":"10.1137","volume":"64","author":[{"given":"Shanshan","family":"Xiao","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing, 100084 China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2169-1491","authenticated-orcid":true,"given":"Pengzhan","family":"Jin","sequence":"additional","affiliation":[{"name":"Corresponding author. National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, 100871 China, and Chongqing Research Institute of Big Data, Peking University, Chongqing, 401329, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3301-3487","authenticated-orcid":true,"given":"Yifa","family":"Tang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2026,4,30]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10409-021-01148-1"},{"key":"ref2","unstructured":"J. Deng, X. Li, H. Xiong, X. Hu, and J. Ma, Geometry-guided conditional adaption for surrogate models of large-scale 3d PDEs on arbitrary geometries, https:\/\/openreview.net\/forum?id=EyQO9RPhwN, 2024."},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1951.1.353"},{"key":"ref4","unstructured":"W. E, C. Ma, and L. Wu, Barron Spaces and the Compositional Function Spaces for Neural Network Models, preprint, arXiv:1906.08039, 2019."},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s40304-018-0127-z"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s11004-009-9257-x"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1038\/s42256-022-00569-2"},{"key":"ref8","first-page":"24048","volume":"34","author":"Gupta G.","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.3390\/math7100992"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.117130"},{"key":"ref11","unstructured":"J. He, X. Liu, and J. Xu, MgNO:\u00a0Efficient Parameterization of Linear Operators Via Multigrid, preprint, arXiv:2310.19809, 2023."},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(89)90020-8"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(90)90005-6"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/4086"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/22M1477751"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1080\/17476933.2018.1460822"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-021-00314-5"},{"key":"ref18","first-page":"2","volume-title":"Selected Papers","author":"Lax P. D.","year":"2005"},{"key":"ref19","first-page":"1","volume":"24","author":"Li Z.","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"ref20","unstructured":"Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar, Fourier Neural Operator for Parametric Partial Differential Equations, preprint, arXiv:2010.08895, 2020."},{"key":"ref21","unstructured":"Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar, Neural Operator:\u00a0Graph Kernel Network for Partial Differential Equations, preprint, arXiv:2003.03485, 2020."},{"key":"ref22","unstructured":"L. Lu, P. Jin, and G. E. Karniadakis, DeepONet:\u00a0Learning Nonlinear Operators for Identifying Differential Equations Based on the Universal Approximation Theorem of Operators, preprint, arXiv:1910.03193, 2019."},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1038\/s42256-021-00302-5"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1137\/21M1397908"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/18M1229845"},{"key":"ref26","doi-asserted-by":"crossref","unstructured":"J. J. Park, P. Florence, J. Straub, R. Newcombe, and S. Lovegrove, DeepSDF:\u00a0Learning continuous signed distance functions for shape representation, in Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, 2019, pp. 165\u2013174.","DOI":"10.1109\/CVPR.2019.00025"},{"key":"ref27","unstructured":"C. R. Qi, H. Su, K. Mo, and L. J. Guibas, PointNet:\u00a0Deep learning on point sets for 3d classification and segmentation, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017, pp. 652\u2013660."},{"key":"ref28","volume":"30","author":"Qi C. R.","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref29","unstructured":"M. A. Rahman, Z. E. Ross, and K. Azizzadenesheli, U-no:\u00a0U-shaped Neural Operators, preprint, arXiv:2204.11127, 2022."},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"ref31","volume-title":"ICLR Workshop on Physics for Machine Learning","author":"Raonic B.","year":"2023"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-3903-4"},{"key":"ref33","first-page":"70581","volume":"36","author":"Serrano L.","year":"2023","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2021.12.005"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.08.029"},{"key":"ref36","first-page":"7462","volume":"33","author":"Sitzmann V.","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1256\/qj.05.227"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abi8605"},{"key":"ref39","unstructured":"H. Wu, T. Hu, H. Luo, J. Wang, and M. Long, Solving High-Dimensional PDEs with Latent Spectral Models, preprint, arXiv:2301.12664, 2023."},{"key":"ref40","unstructured":"S. Xiao, P. Jin, and Y. Tang, Learning Solution Operators of PDEs Defined on Varying Domains via MIONet, preprint, arXiv:2402.15097, 2024."},{"key":"ref41","unstructured":"M. Yin, N. Charon, R. Brody, L. Lu, N. Trayanova, and M. Maggioni, DIMON:\u00a0Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains, preprint, arXiv:2402.07250, 2024."},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2025.118022"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/j.est.2023.109244"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:36:58Z","timestamp":1777534618000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M171499X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,30]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4,30]]}},"alternative-id":["10.1137\/24M171499X"],"URL":"https:\/\/doi.org\/10.1137\/24m171499x","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,30]]}}}