{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T22:52:26Z","timestamp":1754261546920,"version":"3.41.0"},"publisher-location":"New York, NY, USA","reference-count":62,"publisher":"ACM","license":[{"start":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T00:00:00Z","timestamp":1691107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62106116"],"award-info":[{"award-number":["62106116"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62206291"],"award-info":[{"award-number":["62206291"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,8,6]]},"DOI":"10.1145\/3580305.3599466","type":"proceedings-article","created":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T18:10:58Z","timestamp":1691172658000},"page":"1595-1607","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations"],"prefix":"10.1145","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1794-3657","authenticated-orcid":false,"given":"Yingtao","family":"Luo","sequence":"first","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, PA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9233-3827","authenticated-orcid":false,"given":"Qiang","family":"Liu","sequence":"additional","affiliation":[{"name":"CRIPAC, MAIS, Institute of Automation, Chinese Academy of Sciences, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4566-8197","authenticated-orcid":false,"given":"Yuntian","family":"Chen","sequence":"additional","affiliation":[{"name":"Ningbo Institute of Digital Twin, Eastern Institute of Technology, Ningbo, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0639-2012","authenticated-orcid":false,"given":"Wenbo","family":"Hu","sequence":"additional","affiliation":[{"name":"Hefei University of Technology, Hefei, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5625-215X","authenticated-orcid":false,"given":"Tian","family":"Tian","sequence":"additional","affiliation":[{"name":"RealAI, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6254-2388","authenticated-orcid":false,"given":"Jun","family":"Zhu","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing, China"}]}],"member":"320","published-online":{"date-parts":[[2023,8,4]]},"reference":[{"key":"e_1_3_2_2_1_1","volume-title":"International Conference on Machine Learning. PMLR, 136--145","author":"Amos Brandon","year":"2017","unstructured":"Brandon Amos and J Zico Kolter . 2017 . Optnet: Differentiable optimization as a layer in neural networks . In International Conference on Machine Learning. PMLR, 136--145 . Brandon Amos and J Zico Kolter. 2017. Optnet: Differentiable optimization as a layer in neural networks. In International Conference on Machine Learning. PMLR, 136--145."},{"key":"e_1_3_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1814058116"},{"key":"e_1_3_2_2_3_1","volume-title":"International Conference on Machine Learning. PMLR, 2402--2411","author":"Avila Belbute-Peres Filipe De","year":"2020","unstructured":"Filipe De Avila Belbute-Peres , Thomas Economon , and Zico Kolter . 2020 . Combining differentiable PDE solvers and graph neural networks for fluid flow prediction . In International Conference on Machine Learning. PMLR, 2402--2411 . Filipe De Avila Belbute-Peres, Thomas Economon, and Zico Kolter. 2020. Combining differentiable PDE solvers and graph neural networks for fluid flow prediction. In International Conference on Machine Learning. PMLR, 2402--2411."},{"key":"e_1_3_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0609476104"},{"key":"e_1_3_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1517384113"},{"key":"e_1_3_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1906995116"},{"key":"e_1_3_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110624"},{"key":"e_1_3_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.4.023174"},{"key":"e_1_3_2_2_9_1","volume-title":"Integration of knowledge and data in machine learning. arXiv preprint arXiv:2202.10337","author":"Chen Yuntian","year":"2022","unstructured":"Yuntian Chen and Dongxiao Zhang . 2022. Integration of knowledge and data in machine learning. arXiv preprint arXiv:2202.10337 ( 2022 ). Yuntian Chen and Dongxiao Zhang. 2022. Integration of knowledge and data in machine learning. arXiv preprint arXiv:2202.10337 (2022)."},{"key":"e_1_3_2_2_10_1","volume-title":"Physics-informed learning of governing equations from scarce data. Nature communications","author":"Chen Zhao","year":"2021","unstructured":"Zhao Chen , Yang Liu , and Hao Sun . 2021b. Physics-informed learning of governing equations from scarce data. Nature communications , Vol. 12 , 1 ( 2021 ), 1--13. Zhao Chen, Yang Liu, and Hao Sun. 2021b. Physics-informed learning of governing equations from scarce data. Nature communications, Vol. 12, 1 (2021), 1--13."},{"key":"e_1_3_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1029\/JZ071i020p04785"},{"key":"e_1_3_2_2_12_1","first-page":"17429","article-title":"Discovering symbolic models from deep learning with inductive biases","volume":"33","author":"Cranmer Miles","year":"2020","unstructured":"Miles Cranmer , Alvaro Sanchez Gonzalez , Peter Battaglia , Rui Xu , Kyle Cranmer , David Spergel , and Shirley Ho . 2020 . Discovering symbolic models from deep learning with inductive biases . Advances in Neural Information Processing Systems , Vol. 33 (2020), 17429 -- 17442 . Miles Cranmer, Alvaro Sanchez Gonzalez, Peter Battaglia, Rui Xu, Kyle Cranmer, David Spergel, and Shirley Ho. 2020. Discovering symbolic models from deep learning with inductive biases. Advances in Neural Information Processing Systems, Vol. 33 (2020), 17429--17442.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00962824"},{"key":"e_1_3_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.110079"},{"key":"e_1_3_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.114502"},{"key":"e_1_3_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109056"},{"key":"e_1_3_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2939672.2939738"},{"key":"e_1_3_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1718942115"},{"key":"e_1_3_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.255"},{"key":"e_1_3_2_2_20_1","volume-title":"International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=aUX5Plaq7Oy","author":"Iakovlev Valerii","year":"2021","unstructured":"Valerii Iakovlev , Markus Heinonen , and Harri L\u00e4hdesm\u00e4ki . 2021 . Learning continuous-time PDE s from sparse data with graph neural networks . In International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=aUX5Plaq7Oy Valerii Iakovlev, Markus Heinonen, and Harri L\u00e4hdesm\u00e4ki. 2021. Learning continuous-time PDE s from sparse data with graph neural networks. In International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=aUX5Plaq7Oy"},{"key":"e_1_3_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-021-00314-5"},{"key":"e_1_3_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2020.3017010"},{"key":"e_1_3_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2101784118"},{"key":"e_1_3_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2016.803"},{"key":"e_1_3_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/72.712178"},{"key":"e_1_3_2_2_26_1","volume-title":"Deep Learning For Symbolic Mathematics. In International Conference on Learning Representations.","author":"Lample Guillaume","year":"2019","unstructured":"Guillaume Lample and Francc ois Charton . 2019 . Deep Learning For Symbolic Mathematics. In International Conference on Learning Representations. Guillaume Lample and Francc ois Charton. 2019. Deep Learning For Symbolic Mathematics. In International Conference on Learning Representations."},{"key":"e_1_3_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90007-N"},{"key":"e_1_3_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/3447548.3467448"},{"key":"e_1_3_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v34i01.5420"},{"key":"e_1_3_2_2_30_1","volume-title":"Learning Compositional Koopman Operators for Model-Based Control. In International Conference on Learning Representations.","author":"Li Yunzhu","year":"2019","unstructured":"Yunzhu Li , Hao He , Jiajun Wu , Dina Katabi , and Antonio Torralba . 2019 . Learning Compositional Koopman Operators for Model-Based Control. In International Conference on Learning Representations. Yunzhu Li, Hao He, Jiajun Wu, Dina Katabi, and Antonio Torralba. 2019. Learning Compositional Koopman Operators for Model-Based Control. In International Conference on Learning Representations."},{"key":"e_1_3_2_2_31_1","volume-title":"International Conference on Learning Representations.","author":"Li Yunzhu","year":"2018","unstructured":"Yunzhu Li , Jiajun Wu , Russ Tedrake , Joshua B Tenenbaum , and Antonio Torralba . 2018 . Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids . In International Conference on Learning Representations. Yunzhu Li, Jiajun Wu, Russ Tedrake, Joshua B Tenenbaum, and Antonio Torralba. 2018. Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids. In International Conference on Learning Representations."},{"key":"e_1_3_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.5555\/3495724.3496291"},{"key":"e_1_3_2_2_33_1","volume-title":"Fourier Neural Operator for Parametric Partial Differential Equations. In International Conference on Learning Representations.","author":"Li Zongyi","year":"2020","unstructured":"Zongyi Li , Nikola Borislavov Kovachki , Kamyar Azizzadenesheli , Kaushik Bhattacharya , Andrew Stuart , Anima Anandkumar , 2020 a. Fourier Neural Operator for Parametric Partial Differential Equations. In International Conference on Learning Representations. Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar, et al. 2020a. Fourier Neural Operator for Parametric Partial Differential Equations. In International Conference on Learning Representations."},{"key":"e_1_3_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.108925"},{"key":"e_1_3_2_2_35_1","volume-title":"International Conference on Machine Learning. PMLR, 3208--3216","author":"Long Zichao","year":"2018","unstructured":"Zichao Long , Yiping Lu , Xianzhong Ma , and Bin Dong . 2018 . Pde-net: Learning pdes from data . In International Conference on Machine Learning. PMLR, 3208--3216 . Zichao Long, Yiping Lu, Xianzhong Ma, and Bin Dong. 2018. Pde-net: Learning pdes from data. In International Conference on Machine Learning. PMLR, 3208--3216."},{"key":"e_1_3_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1038\/s42256-021-00302-5"},{"key":"e_1_3_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/3534678.3539245"},{"key":"e_1_3_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.5555\/3327144.3327321"},{"key":"e_1_3_2_2_39_1","volume-title":"Proceedings of the 32nd International Conference on Neural Information Processing Systems. 9278--9288","author":"Morton Jeremy","year":"2018","unstructured":"Jeremy Morton , Freddie D Witherden , Antony Jameson , and Mykel J Kochenderfer . 2018 . Deep dynamical modeling and control of unsteady fluid flows . In Proceedings of the 32nd International Conference on Neural Information Processing Systems. 9278--9288 . Jeremy Morton, Freddie D Witherden, Antony Jameson, and Mykel J Kochenderfer. 2018. Deep dynamical modeling and control of unsteady fluid flows. In Proceedings of the 32nd International Conference on Neural Information Processing Systems. 9278--9288."},{"key":"e_1_3_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.11.039"},{"key":"e_1_3_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"e_1_3_2_2_42_1","volume-title":"International Conference on Learning Representations.","author":"Rao Chengping","year":"2022","unstructured":"Chengping Rao , Pu Ren , Yang Liu , and Hao Sun . 2022 . Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning . In International Conference on Learning Representations. Chengping Rao, Pu Ren, Yang Liu, and Hao Sun. 2022. Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning. In International Conference on Learning Representations."},{"key":"e_1_3_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)EM.1943-7889.0001947"},{"key":"e_1_3_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1137\/18M1191944"},{"key":"e_1_3_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.1602614"},{"key":"e_1_3_2_2_46_1","volume-title":"International Conference on Machine Learning. PMLR, 4442--4450","author":"Sahoo Subham","year":"2018","unstructured":"Subham Sahoo , Christoph Lampert , and Georg Martius . 2018 . Learning equations for extrapolation and control . In International Conference on Machine Learning. PMLR, 4442--4450 . Subham Sahoo, Christoph Lampert, and Georg Martius. 2018. Learning equations for extrapolation and control. In International Conference on Machine Learning. PMLR, 4442--4450."},{"key":"e_1_3_2_2_47_1","volume-title":"International Conference on Machine Learning. PMLR, 8459--8468","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 International Conference on Machine Learning. PMLR, 8459--8468 . Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter Battaglia. 2020. Learning to simulate complex physics with graph networks. In International Conference on Machine Learning. PMLR, 8459--8468."},{"key":"e_1_3_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2016.0446"},{"key":"e_1_3_2_2_49_1","volume-title":"Science","volume":"324","author":"Schmidt Michael","year":"2009","unstructured":"Michael Schmidt and Hod Lipson . 2009 . Distilling free-form natural laws from experimental data . Science , Vol. 324 , 5923 (2009), 81--85. Michael Schmidt and Hod Lipson. 2009. Distilling free-form natural laws from experimental data. Science, Vol. 324, 5923 (2009), 81--85."},{"key":"e_1_3_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.08.029"},{"key":"e_1_3_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v35i11.17164"},{"key":"e_1_3_2_2_52_1","volume-title":"34nd Conference on Neural Information Processing Systems.","author":"Um Kiwon","year":"2020","unstructured":"Kiwon Um , Robert Brand , Philipp Holl , Nils Thuerey , 2020 . Solver-in-the-loop: Learning from differentiable physics to interact with iterative PDE-solvers . In 34nd Conference on Neural Information Processing Systems. Kiwon Um, Robert Brand, Philipp Holl, Nils Thuerey, et al. 2020. Solver-in-the-loop: Learning from differentiable physics to interact with iterative PDE-solvers. In 34nd Conference on Neural Information Processing Systems."},{"key":"e_1_3_2_2_53_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. 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_3_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jhydrol.2020.124700"},{"key":"e_1_3_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/3394486.3403198"},{"key":"e_1_3_2_2_56_1","volume-title":"Dl-pde: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data. arXiv preprint arXiv:1908.04463","author":"Xu Hao","year":"2019","unstructured":"Hao Xu , Haibin Chang , and Dongxiao Zhang . 2019 . Dl-pde: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data. arXiv preprint arXiv:1908.04463 (2019). Hao Xu, Haibin Chang, and Dongxiao Zhang. 2019. Dl-pde: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data. arXiv preprint arXiv:1908.04463 (2019)."},{"key":"e_1_3_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109584"},{"key":"e_1_3_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0042868"},{"volume-title":"Stochastic methods for flow in porous media: coping with uncertainties","author":"Zhang Dongxiao","key":"e_1_3_2_2_59_1","unstructured":"Dongxiao Zhang . 2001. Stochastic methods for flow in porous media: coping with uncertainties . Elsevier . Dongxiao Zhang. 2001. Stochastic methods for flow in porous media: coping with uncertainties. Elsevier."},{"key":"e_1_3_2_2_60_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.09.015"},{"key":"e_1_3_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.04.018"},{"key":"e_1_3_2_2_62_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.05.024"}],"event":{"name":"KDD '23: The 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining","sponsor":["SIGMOD ACM Special Interest Group on Management of Data","SIGKDD ACM Special Interest Group on Knowledge Discovery in Data"],"location":"Long Beach CA USA","acronym":"KDD '23"},"container-title":["Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3580305.3599466","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3580305.3599466","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T16:37:37Z","timestamp":1750178257000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3580305.3599466"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,4]]},"references-count":62,"alternative-id":["10.1145\/3580305.3599466","10.1145\/3580305"],"URL":"https:\/\/doi.org\/10.1145\/3580305.3599466","relation":{},"subject":[],"published":{"date-parts":[[2023,8,4]]},"assertion":[{"value":"2023-08-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}