{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T08:18:57Z","timestamp":1783066737162,"version":"3.54.6"},"reference-count":74,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T00:00:00Z","timestamp":1783036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>This paper presents a highly efficient and robust differentiable flu::id framework, centered on a novel surrogate gradient method that utilizes the flow map structural advantages. Our key insight reveals a significant misalignment between computational intensity and gradient importance during the backward pass. Specifically, we identify a physical duality within the adjoint process, revealing that the cross-step connections inherent in the flow map act as dominant gradient \"highways\" that propagate sensitivities over long horizons with high fidelity. Leveraging these insights, we develop a surrogate gradient model that retains these critical connections while pruning redundant adjoint computations in a physics-informed manner. Integrated with tailored acceleration techniques, our framework is successfully applied to diverse, challenging optimization tasks characterized by long time horizons and rich vorticity. Results demonstrate significant speedups and memory reductions while maintaining nearly-identical gradients compared to the full-gradient baseline.<\/jats:p>","DOI":"10.1145\/3811337","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["DiffSurFlow: Efficient and Robust Differentiable Fluid Optimization via Surrogate Strategy on Flow Map"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-9345-4887","authenticated-orcid":false,"given":"Yuhao","family":"Quan","sequence":"first","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4554-0719","authenticated-orcid":false,"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-4746-3895","authenticated-orcid":false,"given":"Weile","family":"Lian","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2988-8252","authenticated-orcid":false,"given":"Zhi","family":"Wang","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5378-4003","authenticated-orcid":false,"given":"Xubo","family":"Yang","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University, Shanghai, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2024.109187"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555517"},{"key":"e_1_2_1_3_1","volume-title":"Van Emden Henson, and Steve F. McCormick","author":"Briggs William L.","year":"2000","unstructured":"William L. Briggs, Van Emden Henson, and Steve F. McCormick. 2000. A multigrid tutorial (2nd ed.). Society for Industrial and Applied Mathematics, USA.","edition":"2"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/3687959"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3757377.3763997"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/3641519.3657468"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3624011"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530169"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.2172\/87798"},{"key":"e_1_2_1_10_1","volume-title":"Learning Vortex Dynamics for Fluid Inference and Prediction. In The Eleventh International Conference on Learning Representations, ICLR 2023","author":"Deng Yitong","year":"2023","unstructured":"Yitong Deng, Hong-Xing Yu, Jiajun Wu, and Bo Zhu. 2023a. Learning Vortex Dynamics for Fluid Inference and Prediction. In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1\u20135, 2023. OpenReview.net. https:\/\/openreview.net\/forum?id=nYWqxUwFc3x"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618392"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2021.3070305"},{"key":"e_1_2_1_13_1","first-page":"1","article-title":"Diffpd: Differentiable projective dynamics","volume":"41","author":"Du Tao","year":"2021","unstructured":"Tao Du, Kui Wu, Pingchuan Ma, Sebastien Wah, Andrew Spielberg, Daniela Rus, and Wojciech Matusik. 2021b. Diffpd: Differentiable projective dynamics. ACM Transactions on Graphics (ToG) 41, 2 (2021), 1\u201321.","journal-title":"ACM Transactions on Graphics (ToG)"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417795"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275044"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","unstructured":"Tianhong Gao Xuwen Chen Xingqiao Li Wei Li Baoquan Chen Zherong Pan Kui Wu and Mengyu Chu. 2025a. Fast Multi-Body Coupling for Underwater Interactions. In Pacific Graphics Conference Papers Posters and Demos Marc Christie Ping-Hsuan Han Shih-Syun Lin Nico Pietroni Teseo Schneider Hsin-Ruey Tsai Yu-Shuen Wang and Eugene Zhang (Eds.). The Eurographics Association. 10.2312\/pg.20251268","DOI":"10.2312\/pg.20251268"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52734.2025.02430"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417766"},{"key":"e_1_2_1_19_1","volume-title":"An introduction to the adjoint approach to design. Flow, turbulence and combustion 65, 3","author":"Giles Michael B","year":"2000","unstructured":"Michael B Giles and Niles A Pierce. 2000. An introduction to the adjoint approach to design. Flow, turbulence and combustion 65, 3 (2000), 393\u2013415."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-021-01453-z"},{"key":"e_1_2_1_21_1","volume-title":"NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fields. In International Conference on Machine Learning, ICML 2022","volume":"7929","author":"Guan Shanyan","year":"2022","unstructured":"Shanyan Guan, Huayu Deng, Yunbo Wang, and Xiaokang Yang. 2022. NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fields. In International Conference on Machine Learning, ICML 2022, 17\u201323 July 2022, Baltimore, Maryland, USA (Proceedings of Machine Learning Research, Vol. 162), Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesv\u00e1ri, Gang Niu, and Sivan Sabato (Eds.). PMLR, 7919\u20137929. https:\/\/proceedings.mlr.press\/v162\/guan22a.html"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459799"},{"key":"e_1_2_1_23_1","volume-title":"The CMA evolution strategy: a comparing review. Towards a new evolutionary computation: Advances in the estimation of distribution algorithms","author":"Hansen Nikolaus","year":"2006","unstructured":"Nikolaus Hansen. 2006. The CMA evolution strategy: a comparing review. Towards a new evolutionary computation: Advances in the estimation of distribution algorithms (2006), 75\u2013102."},{"key":"e_1_2_1_24_1","volume-title":"NeurIPS workshop","volume":"2","author":"Holl Philipp","year":"2020","unstructured":"Philipp Holl, Vladlen Koltun, Kiwon Um, and Nils Thuerey. 2020. phiflow: A differentiable pde solving framework for deep learning via physical simulations. In NeurIPS workshop, Vol. 2."},{"key":"e_1_2_1_25_1","volume-title":"TensorFlow and Jax. In International Conference on Machine Learning. PMLR.","author":"Holl Philipp","year":"2024","unstructured":"Philipp Holl and Nils Thuerey. 2024. \u03a6Flow (PhiFlow): Differentiable Simulations for PyTorch, TensorFlow and Jax. In International Conference on Machine Learning. PMLR."},{"key":"e_1_2_1_26_1","volume-title":"Conference on Neural Information Processing Systems (NeurIPS).","author":"Hu Changyu","year":"2025","unstructured":"Changyu Hu, Yanke Qu, Qiuan Yang, Xiaoyu Xiong, Kui Wu, Wei Li, and Tao Du. 2025. Learning to Control Free-Form Soft Swimmers. In Conference on Neural Information Processing Systems (NeurIPS)."},{"key":"e_1_2_1_27_1","unstructured":"Yuanming Hu Luke Anderson Tzu-Mao Li Qi Sun Nathan Carr Jonathan Ragan-Kelley and Fredo Durand. 2020. DiffTaichi: Differentiable Programming for Physical Simulation. https:\/\/openreview.net\/forum?id=B1eB5xSFvr"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01061285"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356560"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392473"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13619"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/3687899"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.paerosci.2022.100849"},{"key":"e_1_2_1_34_1","volume-title":"MPMNet: A data-driven MPM framework for dynamic fluid-solid interaction","author":"Li Jin","year":"2023","unstructured":"Jin Li, Yang Gao, Ju Dai, Shuai Li, Aimin Hao, and Hong Qin. 2023a. MPMNet: A data-driven MPM framework for dynamic fluid-solid interaction. IEEE Transactions on Visualization and Computer Graphics (2023)."},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555429"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.52202\/079017-2697"},{"key":"e_1_2_1_37_1","volume-title":"Lagrangian Covector Fluid with Free Surface. In ACM SIGGRAPH 2024 Conference Papers. 1\u201310","author":"Li Zhiqi","year":"2024","unstructured":"Zhiqi Li, Barnab\u00e1s B\u00f6rcs\u00f6k, Duowen Chen, Yutong Sun, Bo Zhu, and Greg Turk. 2024a. Lagrangian Covector Fluid with Free Surface. In ACM SIGGRAPH 2024 Conference Papers. 1\u201310."},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/3757377.3763903"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618318"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA46639.2022.9812066"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275035"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015744"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530120"},{"key":"e_1_2_1_44_1","volume-title":"International Conference on Machine Learning. PMLR, 16413\u201316427","author":"Nava Elvis","year":"2022","unstructured":"Elvis Nava, John Z Zhang, Mike Yan Michelis, Tao Du, Pingchuan Ma, Benjamin F Grewe, Wojciech Matusik, and Robert Kevin Katzschmann. 2022. Fast aquatic swimmer optimization with differentiable projective dynamics and neural network hydrodynamic models. In International Conference on Machine Learning. PMLR, 16413\u201316427."},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2019.2931595"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.08.032"},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3016963"},{"key":"e_1_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.52202\/068431-0500"},{"key":"e_1_2_1_49_1","volume-title":"Proceedings of the 37th International Conference on Machine Learning (Proceedings of Machine Learning Research","author":"Sanchez-Gonzalez Alvaro","year":"2020","unstructured":"Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter Battaglia. 2020. Learning to Simulate Complex Physics with Graph Networks. In Proceedings of the 37th International Conference on Machine Learning (Proceedings of Machine Learning Research, Vol. 119), Hal Daum\u00e9 III and Aarti Singh (Eds.). PMLR, 8459\u20138468. https:\/\/proceedings.mlr.press\/v119\/sanchez-gonzalez20a.html"},{"key":"e_1_2_1_50_1","volume-title":"Proceedings of The 2nd Conference on Robot Learning (Proceedings of Machine Learning Research","volume":"335","author":"Schenck Connor","year":"2018","unstructured":"Connor Schenck and Dieter Fox. 2018. SPNets: Differentiable Fluid Dynamics for Deep Neural Networks. In Proceedings of The 2nd Conference on Robot Learning (Proceedings of Machine Learning Research, Vol. 87), Aude Billard, Anca Dragan, Jan Peters, and Jun Morimoto (Eds.). PMLR, 317\u2013335. https:\/\/proceedings.mlr.press\/v87\/schenck18a.html"},{"key":"e_1_2_1_51_1","volume-title":"Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347","author":"Schulman John","year":"2017","unstructured":"John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. 2017. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347 (2017)."},{"key":"e_1_2_1_52_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2008.05.009"},{"key":"e_1_2_1_53_1","unstructured":"Arthur St\u00fcck. 2012. Adjoint Navier-Stokes methods for hydrodynamic shape optimisation. Technische Universit\u00e4t Hamburg."},{"key":"e_1_2_1_54_1","doi-asserted-by":"publisher","DOI":"10.1145\/3606923"},{"key":"e_1_2_1_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/3687963"},{"key":"e_1_2_1_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/3731180"},{"key":"e_1_2_1_57_1","doi-asserted-by":"publisher","DOI":"10.1609\/AAAI.V35I7.16764"},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.142637"},{"key":"e_1_2_1_59_1","volume-title":"Proceedings of the 34th International Conference on Machine Learning -","volume":"70","author":"Tompson Jonathan","year":"2017","unstructured":"Jonathan Tompson, Kristofer Schlachter, Pablo Sprechmann, and Ken Perlin. 2017. Accelerating eulerian fluid simulation with convolutional networks. In Proceedings of the 34th International Conference on Machine Learning - Volume 70 (Sydney, NSW, Australia) (ICML'17). JMLR.org, 3424\u20133433."},{"key":"e_1_2_1_60_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882337"},{"key":"e_1_2_1_61_1","volume-title":"International Conference on Learning Representations.","author":"Ummenhofer Benjamin","year":"2019","unstructured":"Benjamin Ummenhofer, Lukas Prantl, Nils Thuerey, and Vladlen Koltun. 2019. Lagrangian fluid simulation with continuous convolutions. In International Conference on Learning Representations."},{"key":"e_1_2_1_62_1","doi-asserted-by":"publisher","DOI":"10.1145\/3687996"},{"key":"e_1_2_1_63_1","doi-asserted-by":"publisher","DOI":"10.1145\/3731198"},{"key":"e_1_2_1_64_1","doi-asserted-by":"publisher","DOI":"10.1145\/3641519.3657483"},{"key":"e_1_2_1_65_1","doi-asserted-by":"publisher","DOI":"10.1029\/WR012i005p00971"},{"key":"e_1_2_1_66_1","volume-title":"Fluidlab: A differentiable environment for benchmarking complex fluid manipulation. arXiv preprint arXiv:2303.02346","author":"Xian Zhou","year":"2023","unstructured":"Zhou Xian, Bo Zhu, Zhenjia Xu, Hsiao-Yu Tung, Antonio Torralba, Katerina Fragkiadaki, and Chuang Gan. 2023. Fluidlab: A differentiable environment for benchmarking complex fluid manipulation. arXiv preprint arXiv:2303.02346 (2023)."},{"key":"e_1_2_1_67_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2018.2873375"},{"key":"e_1_2_1_68_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530150"},{"key":"e_1_2_1_69_1","doi-asserted-by":"publisher","DOI":"10.1002\/cav.1695"},{"key":"e_1_2_1_70_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109781"},{"key":"e_1_2_1_71_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111876"},{"key":"e_1_2_1_72_1","doi-asserted-by":"publisher","DOI":"10.52202\/075280-2777"},{"key":"e_1_2_1_73_1","doi-asserted-by":"publisher","DOI":"10.1145\/3658180"},{"key":"e_1_2_1_74_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3095815"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:49:23Z","timestamp":1783064963000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3811337"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,3]]},"references-count":74,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,7,3]]}},"alternative-id":["10.1145\/3811337"],"URL":"https:\/\/doi.org\/10.1145\/3811337","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,3]]},"assertion":[{"value":"2026-01-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-03-27","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-03","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}