{"intvolume":"       267","author":[{"full_name":"Pervez, Adeel A","last_name":"Pervez","first_name":"Adeel A","id":"fca6d90c-d47f-11ee-bc87-93ff51604981"},{"full_name":"Gavves, Efstratios","first_name":"Efstratios","last_name":"Gavves"},{"id":"26cfd52f-2483-11ee-8040-88983bcc06d4","first_name":"Francesco","last_name":"Locatello","orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco"}],"status":"public","abstract":[{"lang":"eng","text":"We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in neural network hidden representations. The represented PDEs are then solved and decoded for specific tasks. The learned PDE representations naturally express the spatiotemporal dynamics in data in neural network hidden space, enabling increased modeling power. Solving the PDE representations in a compute and memory-efficient way, however, is a significant challenge. We develop a native, GPU-capable, parallel, sparse and differentiable multigrid solver specialized for linear partial differential equations that acts as a module in Mechanistic PDE Networks. Leveraging the PDE solver we propose a discovery architecture that can discovers nonlinear PDEs in complex settings, while being robust to noise. We validate PDE discovery on a number of PDEs including reaction-diffusion and Navier-Stokes equations."}],"day":"01","has_accepted_license":"1","OA_place":"publisher","month":"05","publication_identifier":{"eissn":["2640-3498"]},"ddc":["000"],"publisher":"ML Research Press","year":"2025","department":[{"_id":"FrLo"}],"alternative_title":["PMLR"],"acknowledgement":"AP. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.\r\nFL. This research was funded in whole or in part by the Austrian Science Fund (FWF) 10.55776/COE12. For open access purposes, the author has applied a CC BY public\r\ncopyright license to any author accepted manuscript version arising from this submission.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"48962-48973","publication":"42nd International Conference on Machine Learning","conference":{"end_date":"2025-07-19","name":"ICML: International Conference on Machine Learning","location":"Vancouver, Canada","start_date":"2025-07-13"},"file_date_updated":"2025-12-16T12:21:49Z","date_created":"2025-12-14T23:02:04Z","OA_type":"gold","language":[{"iso":"eng"}],"volume":267,"scopus_import":"1","oa":1,"arxiv":1,"ec_funded":1,"related_material":{"link":[{"relation":"software","url":"https://github.com/ alpz/mech-nn-discovery-pde"}]},"oa_version":"Published Version","date_updated":"2025-12-16T12:24:55Z","corr_author":"1","external_id":{"arxiv":["2502.18377"]},"file":[{"relation":"main_file","access_level":"open_access","file_id":"20827","content_type":"application/pdf","creator":"dernst","date_updated":"2025-12-16T12:21:49Z","file_size":993381,"checksum":"933cb673fb41416f537278fb990df6c3","date_created":"2025-12-16T12:21:49Z","file_name":"2025_ICML_Pervez.pdf","success":1}],"date_published":"2025-05-01T00:00:00Z","citation":{"ieee":"A. A. Pervez, E. Gavves, and F. Locatello, “Mechanistic PDE networks for discovery of governing equations,” in <i>42nd International Conference on Machine Learning</i>, Vancouver, Canada, 2025, vol. 267, pp. 48962–48973.","apa":"Pervez, A. A., Gavves, E., &#38; Locatello, F. (2025). Mechanistic PDE networks for discovery of governing equations. In <i>42nd International Conference on Machine Learning</i> (Vol. 267, pp. 48962–48973). Vancouver, Canada: ML Research Press.","chicago":"Pervez, Adeel A, Efstratios Gavves, and Francesco Locatello. “Mechanistic PDE Networks for Discovery of Governing Equations.” In <i>42nd International Conference on Machine Learning</i>, 267:48962–73. ML Research Press, 2025.","short":"A.A. Pervez, E. Gavves, F. Locatello, in:, 42nd International Conference on Machine Learning, ML Research Press, 2025, pp. 48962–48973.","mla":"Pervez, Adeel A., et al. “Mechanistic PDE Networks for Discovery of Governing Equations.” <i>42nd International Conference on Machine Learning</i>, vol. 267, ML Research Press, 2025, pp. 48962–73.","ama":"Pervez AA, Gavves E, Locatello F. Mechanistic PDE networks for discovery of governing equations. In: <i>42nd International Conference on Machine Learning</i>. Vol 267. ML Research Press; 2025:48962-48973.","ista":"Pervez AA, Gavves E, Locatello F. 2025. Mechanistic PDE networks for discovery of governing equations. 42nd International Conference on Machine Learning. ICML: International Conference on Machine Learning, PMLR, vol. 267, 48962–48973."},"type":"conference","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"title":"Mechanistic PDE networks for discovery of governing equations","_id":"20817","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"quality_controlled":"1","publication_status":"published","article_processing_charge":"No"}