{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T11:47:38Z","timestamp":1782128858761,"version":"3.54.5"},"reference-count":45,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T00:00:00Z","timestamp":1782086400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T00:00:00Z","timestamp":1782086400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["advanced.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Advanced Science"],"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Ring origami, consisting of closed\u2010loop rods, can realize diverse shape\u2010morphing behaviors, including 2D\u2010to\u20101D, 2D\u2010to\u20102D, and 2D\u2010to\u20103D transformations, by harnessing snap\u2010buckling instability. To broaden its application potential in areas such as deployable aerospace structures, soft robotics, and reconfigurable metamaterials, a programmable design framework is highly desired. In this work, we develop a unified framework for the forward prediction and inverse design of ring origami by integrating Kirchhoff rod theory with a physics\u2010informed neural network. The framework can identify the stable states of various segmented rings (e.g., square and hexagonal rings) composed of rod segments with prescribed constant or varying natural curvature (i.e., curvature in the stress\u2010free state). By introducing an additional shape\u2010matching loss, the framework can also determine the natural curvature profile of segmented rings required to achieve stable configurations that can be confined within a target spatial domain or conform to a target curved surface. Its generality and robustness are further demonstrated by extending it to 3D rod systems. This work establishes a powerful strategy for the programmable design of elastic rod systems exemplified by ring origami and opens new opportunities for functional applications that demand shape\u2010morphing structures with simple geometries, high packing capability, and prescribed stable configurations.<\/jats:p>","DOI":"10.1002\/advs.76194","type":"journal-article","created":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T10:58:02Z","timestamp":1782125882000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Physics\u2010Informed Neural Network\u2010Enabled Forward Prediction and Inverse Design of Ring Origami"],"prefix":"10.1002","author":[{"given":"Luyuan","family":"Ning","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering Stanford University  Stanford California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lu","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering Stanford University  Stanford California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sophie","family":"Leanza","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering Stanford University  Stanford California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9292-5267","authenticated-orcid":false,"given":"Ruike Renee","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering Stanford University  Stanford California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,6,22]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/aisy.202100107"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4056637"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.20517\/ss.2023.42"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41578\u2010025\u201000828\u20109"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10659\u2010015\u20109520\u2010y"},{"issue":"7","key":"e_1_2_9_7_1","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/0020-7683(92)90024-N","article-title":"Elastic Buckling Phenomenon Applicable to Deployable Rings","volume":"29","author":"Goto Y.","year":"1992","journal-title":"International Journal of Solids and Structures"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsolstr.2022.111685"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2405744121"},{"key":"e_1_2_9_10_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.jmps.2023.105407","article-title":"Multiple Equilibrium States of a Curved\u2010Sided Hexagram: Part II\u2014Transitions between States","volume":"180","author":"Lu L.","year":"2023","journal-title":"Journal of the Mechanics and Physics of Solids"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4062221"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2025.106404"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.polymer.2014.08.033"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4054693"},{"key":"e_1_2_9_15_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-7091-2584-7","volume-title":"Deployable Structures","author":"Pellegrino S.","year":"2001"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.11.064069"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.adh5107"},{"issue":"7","key":"e_1_2_9_18_1","doi-asserted-by":"crossref","DOI":"10.1002\/adma.202207372","article-title":"Self\u2010sustained Snapping Drives Autonomous Dancing and Motion in Free\u2010standing Wavy Rings","volume":"35","author":"Zhao Y.","year":"2023","journal-title":"Advanced Materials"},{"key":"e_1_2_9_19_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijmecsci.2025.110746","article-title":"Curved Loop Strip Soft Gripper","volume":"305","author":"Liu W.","year":"2025","journal-title":"International Journal of Mechanical Sciences"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/rpm.20240035"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1002\/adma.202521268"},{"key":"e_1_2_9_22_1","doi-asserted-by":"crossref","unstructured":"S.Leanza J.Lee andR. 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