{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T22:05:36Z","timestamp":1776204336937,"version":"3.50.1"},"reference-count":62,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T00:00:00Z","timestamp":1721347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1846368"],"award-info":[{"award-number":["1846368"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["2313076"],"award-info":[{"award-number":["2313076"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"NSERC","doi-asserted-by":"crossref","award":["Discovery"],"award-info":[{"award-number":["Discovery"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Ontario Early Researchers Award"},{"DOI":"10.13039\/501100001804","name":"Canada Research Chairs","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001804","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2024,7,19]]},"abstract":"<jats:p>The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation undergoing large, nonlinear deformations. We note that every standard geometric representation can be reduced to an occupancy function queried at any point in space, and we define a simulator atop this common interface. For each object, we fit a small implicit neural network encoding spatially varying weights that act as a reduced deformation basis. These weights are trained to learn physically significant motions in the object via random perturbations. Our loss ensures we find a weight-space basis that best minimizes deformation energy by stochastically evaluating elastic energies through Monte Carlo sampling of the deformation volume. At runtime, we simulate in the reduced basis and sample the deformations back to the original domain. Our experiments demonstrate the versatility, accuracy, and speed of this approach on data including signed distance functions, point clouds, neural primitives, tomography scans, radiance fields, Gaussian splats, surface meshes, and volume meshes, as well as showing a variety of material energies, contact models, and time integration schemes.<\/jats:p>","DOI":"10.1145\/3658184","type":"journal-article","created":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T14:47:57Z","timestamp":1721400477000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":16,"title":["Simplicits: Mesh-Free, Geometry-Agnostic Elastic Simulation"],"prefix":"10.1145","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9350-494X","authenticated-orcid":false,"given":"Vismay","family":"Modi","sequence":"first","affiliation":[{"name":"University of Toronto, Toronto, Canada"},{"name":"NVIDIA Research, Toronto, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2130-3735","authenticated-orcid":false,"given":"Nicholas","family":"Sharp","sequence":"additional","affiliation":[{"name":"NVIDIA Research, Seattle, United States of America"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6478-1422","authenticated-orcid":false,"given":"Or","family":"Perel","sequence":"additional","affiliation":[{"name":"NVIDIA Research, Tel Aviv, Israel"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4656-498X","authenticated-orcid":false,"given":"Shinjiro","family":"Sueda","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University, College Station, United States of America"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7079-1934","authenticated-orcid":false,"given":"David I. W.","family":"Levin","sequence":"additional","affiliation":[{"name":"University of Toronto, Toronto, Canada"},{"name":"NVIDIA Research, Toronto, Canada"}]}],"member":"320","published-online":{"date-parts":[[2024,7,19]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3596711.3596792"},{"key":"e_1_2_2_2_1","volume-title":"A finite element method for animating large viscoplastic flow. ACM transactions on graphics (TOG) 26, 3","author":"Bargteil Adam W","year":"2007","unstructured":"Adam W Bargteil, Chris Wojtan, Jessica K Hodgins, and Greg Turk. 2007. A finite element method for animating large viscoplastic flow. ACM transactions on graphics (TOG) 26, 3 (2007), 16--es."},{"key":"e_1_2_2_3_1","volume-title":"Fast Winding Numbers for Soups and Clouds. ACM Transactions on Graphics","author":"Barill Gavin","year":"2018","unstructured":"Gavin Barill, Neil Dickson, Ryan Schmidt, David I.W. Levin, and Alec Jacobson. 2018. Fast Winding Numbers for Soups and Clouds. ACM Transactions on Graphics (2018)."},{"key":"e_1_2_2_4_1","volume-title":"Siddhartha Chaudhuri, Eitan Grinspun, Yi Zhou, and Alec Jacobson.","author":"Benchekroun Otman","year":"2023","unstructured":"Otman Benchekroun, Jiayi Eris Zhang, Siddhartha Chaudhuri, Eitan Grinspun, Yi Zhou, and Alec Jacobson. 2023. Fast Complementary Dynamics via Skinning Eigenmodes. arXiv:2303.11886 [cs.GR]"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1399504.1360662"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3340252"},{"key":"e_1_2_2_8_1","volume-title":"Zhecheng Wang, Maurizio M. Chiaramonte, Kevin Carlberg, and Eitan Grinspun.","author":"Chang Yue","year":"2023","unstructured":"Yue Chang, Peter Yichen Chen, Zhecheng Wang, Maurizio M. Chiaramonte, Kevin Carlberg, and Eitan Grinspun. 2023. LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields. arXiv:2310.15907 [cs.GR]"},{"key":"e_1_2_2_9_1","volume-title":"Simulating Physics with Implicit Neural Spatial Representations. In International Conference on Machine Learning.","author":"Chen Honglin","year":"2023","unstructured":"Honglin Chen, Rundi Wu, Eitan Grinspun, Changxi Zheng, and Peter Yichen Chen. 2023a. Simulating Physics with Implicit Neural Spatial Representations. In International Conference on Machine Learning."},{"key":"e_1_2_2_10_1","volume-title":"CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations. In The Eleventh International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=FUORz1tG8Og","author":"Chen Peter Yichen","year":"2023","unstructured":"Peter Yichen Chen, Jinxu Xiang, Dong Heon Cho, Yue Chang, G A Pershing, Henrique Teles Maia, Maurizio M Chiaramonte, Kevin Thomas Carlberg, and Eitan Grinspun. 2023b. CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations. In The Eleventh International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=FUORz1tG8Og"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566581"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218456"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.5555\/274976.274981"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618352"},{"key":"e_1_2_2_15_1","volume-title":"ACM transactions on graphics (TOG)","author":"Faure Fran\u00e7ois","unstructured":"Fran\u00e7ois Faure, Benjamin Gilles, Guillaume Bousquet, and Dinesh K Pai. 2011. Sparse meshless models of complex deformable solids. In ACM transactions on graphics (TOG), Vol. 30. ACM, 73."},{"key":"e_1_2_2_16_1","doi-asserted-by":"crossref","unstructured":"Yutao Feng Yintong Shang Xuan Li Tianjia Shao Chenfanfu Jiang and Yin Yang. 2023. PIE-NeRF: Physics-based Interactive Elastodynamics with NeRF. arXiv:2311.13099 [cs.CV]","DOI":"10.1109\/CVPR52733.2024.00426"},{"key":"e_1_2_2_17_1","doi-asserted-by":"crossref","unstructured":"Lawson Fulton Vismay Modi David Duvenaud David Levin and Alec Jacobson. 2019. Latent-space Dynamics for Reduced Deformable Simulation.","DOI":"10.1111\/cgf.13645"},{"key":"e_1_2_2_18_1","volume-title":"Realtime, Controllable and Generalisable Animation of Volumetric Representations. arXiv preprint arXiv:2208.00949","author":"Garbin Stephan J","year":"2022","unstructured":"Stephan J Garbin, Marek Kowalski, Virginia Estellers, Stanislaw Szymanowicz, Shideh Rezaeifar, Jingjing Shen, Matthew Johnson, and Julien Valentin. 2022. VolTeMorph: Realtime, Controllable and Generalisable Animation of Volumetric Representations. arXiv preprint arXiv:2208.00949 (2022)."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2459687"},{"key":"e_1_2_2_20_1","first-page":"1","article-title":"Taichi: a language for high-performance computation on spatially sparse data structures","volume":"38","author":"Hu Yuanming","year":"2019","unstructured":"Yuanming Hu, Tzu-Mao Li, Luke Anderson, Jonathan Ragan-Kelley, and Fr\u00e9do Durand. 2019. Taichi: a language for high-performance computation on spatially sparse data structures. ACM Transactions on Graphics (TOG) 38, 6 (2019), 1--16.","journal-title":"ACM Transactions on Graphics (TOG)"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201353"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897826.2927348"},{"key":"e_1_2_2_23_1","volume-title":"Harmonic coordinates for character articulation. ACM transactions on graphics (TOG) 26, 3","author":"Joshi Pushkar","year":"2007","unstructured":"Pushkar Joshi, Mark Meyer, Tony DeRose, Brian Green, and Tom Sanocki. 2007. Harmonic coordinates for character articulation. ACM transactions on graphics (TOG) 26, 3 (2007), 71--es."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/3592433"},{"key":"e_1_2_2_25_1","volume-title":"Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980","author":"Kingma Diederik P","year":"2014","unstructured":"Diederik P Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)."},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","unstructured":"Shanah Kirk Yueh Lee Fabiano R. Lucchesi Natalia D. Aredes Nicholas Gruszauskas James Catto Kimberly Garcia Rose Jarosz Vinay Duddalwar Bino Varghese Kimberly Rieger-Christ and John Lemmerman. 2016. The Cancer Genome Atlas Urothelial Bladder Carcinoma Collection (TCGA-BLCA). 10.7937\/K9\/TCIA.2016.8LNG8XDR","DOI":"10.7937\/K9\/TCIA.2016.8LNG8XDR"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/3480142"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.5555\/AAI28114599"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392425"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459767"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52729.2023.00037"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417853"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/2994258.2994272"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778776"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/1964921.1964967"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.01032"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-58452-8_24"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/1028523.1028542"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530127"},{"key":"e_1_2_2_40_1","unstructured":"National Library of Medicine. 2005. Visible Human Project CT."},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/1576246.1531358"},{"key":"e_1_2_2_42_1","volume-title":"Wright","author":"Nocedal Jorge","year":"2006","unstructured":"Jorge Nocedal and Stephen J. Wright. 2006. Numerical Optimization (2e ed.). Springer, New York, NY, USA."},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV48922.2021.00581"},{"key":"e_1_2_2_44_1","unstructured":"Adam Paszke Sam Gross Soumith Chintala Gregory Chanan Edward Yang Zachary DeVito Zeming Lin Alban Desmaison Luca Antiga and Adam Lerer. 2017. Automatic differentiation in pytorch. (2017)."},{"key":"e_1_2_2_45_1","volume-title":"Computer Graphics Forum","author":"Peer Andreas","unstructured":"Andreas Peer, Christoph Gissler, Stefan Band, and Matthias Teschner. 2018. An implicit SPH formulation for incompressible linearly elastic solids. In Computer Graphics Forum, Vol. 37. Wiley Online Library, 135--148."},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.01018"},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2020.3019967"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.00291"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/3313797"},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275067"},{"key":"e_1_2_2_51_1","first-page":"6","article-title":"Nonlinear sphere tracing for rendering deformed signed distance fields","volume":"38","author":"Seyb Dario","year":"2019","unstructured":"Dario Seyb, Alec Jacobson, Derek Nowrouzezahrai, and Wojciech Jarosz. 2019. Nonlinear sphere tracing for rendering deformed signed distance fields. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 38, 6 (Nov. 2019). dffm","journal-title":"ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)"},{"key":"e_1_2_2_52_1","volume-title":"David IW Levin, and Justin Solomon","author":"Sharp Nicholas","year":"2023","unstructured":"Nicholas Sharp, Cristian Romero, Alec Jacobson, Etienne Vouga, Paul G Kry, David IW Levin, and Justin Solomon. 2023. Data-Free Learning of Reduced-Order Kinematics. (2023)."},{"key":"e_1_2_2_53_1","volume-title":"Implicit neural representations with periodic activation functions. Advances in neural information processing systems 33","author":"Sitzmann Vincent","year":"2020","unstructured":"Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein. 2020. Implicit neural representations with periodic activation functions. Advances in neural information processing systems 33 (2020), 7462--7473."},{"key":"e_1_2_2_54_1","article-title":"A Dataset and Explorer for 3D Signed Distance Functions","volume":"11","author":"Takikawa Towaki","year":"2022","unstructured":"Towaki Takikawa, Andrew Glassner, and Morgan McGuire. 2022. A Dataset and Explorer for 3D Signed Distance Functions. Journal of Computer Graphics Techniques (JCGT) 11, 2 (27 April 2022), 1--29. http:\/\/jcgt.org\/published\/0011\/02\/01\/","journal-title":"Journal of Computer Graphics Techniques (JCGT)"},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/3588432.3591516"},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/37402.37427"},{"key":"e_1_2_2_57_1","volume-title":"Subspace Mixed Finite Elements for Real-Time Heterogeneous Elasto-dynamics. In SIGGRAPH Asia 2023 Conference Papers. 1--10","author":"Trusty Ty","year":"2023","unstructured":"Ty Trusty, Otman Benchekroun, Eitan Grinspun, Danny M Kaufman, and David IW Levin. 2023. Subspace Mixed Finite Elements for Real-Time Heterogeneous Elasto-dynamics. In SIGGRAPH Asia 2023 Conference Papers. 1--10."},{"key":"e_1_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3322949"},{"key":"e_1_2_2_59_1","volume-title":"PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics. arXiv preprint arXiv:2311.12198","author":"Xie Tianyi","year":"2023","unstructured":"Tianyi Xie, Zeshun Zong, Yuxing Qiu, Xuan Li, Yutao Feng, Yin Yang, and Chenfanfu Jiang. 2023. PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics. arXiv preprint arXiv:2311.12198 (2023)."},{"key":"e_1_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-19827-4_10"},{"key":"e_1_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52688.2022.01781"},{"key":"e_1_2_2_62_1","first-page":"10368","article-title":"Ntopo: Mesh-free topology optimization using implicit neural representations","volume":"34","author":"Zehnder Jonas","year":"2021","unstructured":"Jonas Zehnder, Yue Li, Stelian Coros, and Bernhard Thomaszewski. 2021. Ntopo: Mesh-free topology optimization using implicit neural representations. Advances in Neural Information Processing Systems 34 (2021), 10368--10381.","journal-title":"Advances in Neural Information Processing Systems"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3658184","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3658184","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3658184","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T00:04:15Z","timestamp":1750291455000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3658184"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,19]]},"references-count":62,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,7,19]]}},"alternative-id":["10.1145\/3658184"],"URL":"https:\/\/doi.org\/10.1145\/3658184","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,19]]},"assertion":[{"value":"2024-07-19","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}