[{"oa_version":"Published Version","corr_author":"1","publication_identifier":{"isbn":["9798331320850"]},"publication_status":"published","author":[{"orcid":"0000-0001-5337-5875","last_name":"Chen","full_name":"Chen, Jiale","id":"4d0a9064-1ff6-11ee-9fa6-ec046c604785","first_name":"Jiale"},{"last_name":"Yao","full_name":"Yao, Dingling","first_name":"Dingling","id":"d3e02e50-48a8-11ee-8f62-c108061797fa"},{"first_name":"Adeel A","id":"fca6d90c-d47f-11ee-bc87-93ff51604981","full_name":"Pervez, Adeel A","last_name":"Pervez"},{"first_name":"Dan-Adrian","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","full_name":"Alistarh, Dan-Adrian","last_name":"Alistarh","orcid":"0000-0003-3650-940X"},{"id":"26cfd52f-2483-11ee-8040-88983bcc06d4","first_name":"Francesco","orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco","last_name":"Locatello"}],"OA_place":"publisher","scopus_import":"1","publisher":"ICLR","has_accepted_license":"1","date_updated":"2025-08-04T08:03:11Z","year":"2025","file":[{"file_name":"2025_ICLR_Chen.pdf","relation":"main_file","checksum":"64cfdb12ae3e4e8ba57b1403e1066776","access_level":"open_access","date_created":"2025-07-22T07:58:22Z","file_id":"20065","date_updated":"2025-07-22T07:58:22Z","success":1,"content_type":"application/pdf","creator":"dernst","file_size":732745}],"external_id":{"arxiv":["2410.06074"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"date_published":"2025-04-01T00:00:00Z","abstract":[{"lang":"eng","text":"We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN."}],"department":[{"_id":"DaAl"},{"_id":"FrLo"}],"language":[{"iso":"eng"}],"arxiv":1,"status":"public","OA_type":"diamond","month":"04","citation":{"apa":"Chen, J., Yao, D., Pervez, A. A., Alistarh, D.-A., &#38; Locatello, F. (2025). Scalable mechanistic neural networks. In <i>13th International Conference on Learning Representations</i> (pp. 63716–63737). Singapore, Singapore: ICLR.","mla":"Chen, Jiale, et al. “Scalable Mechanistic Neural Networks.” <i>13th International Conference on Learning Representations</i>, ICLR, 2025, pp. 63716–37.","ieee":"J. Chen, D. Yao, A. A. Pervez, D.-A. Alistarh, and F. Locatello, “Scalable mechanistic neural networks,” in <i>13th International Conference on Learning Representations</i>, Singapore, Singapore, 2025, pp. 63716–63737.","ista":"Chen J, Yao D, Pervez AA, Alistarh D-A, Locatello F. 2025. Scalable mechanistic neural networks. 13th International Conference on Learning Representations. ICLR: International Conference on Learning Representations, 63716–63737.","ama":"Chen J, Yao D, Pervez AA, Alistarh D-A, Locatello F. Scalable mechanistic neural networks. In: <i>13th International Conference on Learning Representations</i>. ICLR; 2025:63716-63737.","short":"J. Chen, D. Yao, A.A. Pervez, D.-A. Alistarh, F. Locatello, in:, 13th International Conference on Learning Representations, ICLR, 2025, pp. 63716–63737.","chicago":"Chen, Jiale, Dingling Yao, Adeel A Pervez, Dan-Adrian Alistarh, and Francesco Locatello. “Scalable Mechanistic Neural Networks.” In <i>13th International Conference on Learning Representations</i>, 63716–37. ICLR, 2025."},"type":"conference","page":"63716-63737","ddc":["000"],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Scalable mechanistic neural networks","publication":"13th International Conference on Learning Representations","_id":"20032","file_date_updated":"2025-07-22T07:58:22Z","date_created":"2025-07-20T22:02:01Z","conference":{"location":"Singapore, Singapore","end_date":"2025-04-28","name":"ICLR: International Conference on Learning Representations","start_date":"2025-04-24"},"oa":1,"day":"01","related_material":{"link":[{"url":"https://github.com/IST-DASLab/ScalableMNN","relation":"software"}]},"quality_controlled":"1"},{"publication_status":"published","author":[{"first_name":"Adeel A","id":"fca6d90c-d47f-11ee-bc87-93ff51604981","last_name":"Pervez","full_name":"Pervez, Adeel A"},{"last_name":"Gavves","full_name":"Gavves, Efstratios","first_name":"Efstratios"},{"id":"26cfd52f-2483-11ee-8040-88983bcc06d4","first_name":"Francesco","orcid":"0000-0002-4850-0683","last_name":"Locatello","full_name":"Locatello, Francesco"}],"OA_place":"publisher","scopus_import":"1","publisher":"ML Research Press","date_updated":"2026-09-16T07:17:18Z","has_accepted_license":"1","volume":267,"year":"2025","oa_version":"Published Version","corr_author":"1","publication_identifier":{"eissn":["2640-3498"]},"date_published":"2025-05-01T00:00:00Z","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."}],"department":[{"_id":"FrLo"}],"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.","language":[{"iso":"eng"}],"arxiv":1,"file":[{"file_name":"2025_ICML_Pervez.pdf","relation":"main_file","checksum":"933cb673fb41416f537278fb990df6c3","date_created":"2025-12-16T12:21:49Z","access_level":"open_access","success":1,"file_id":"20827","date_updated":"2025-12-16T12:21:49Z","content_type":"application/pdf","creator":"dernst","file_size":993381}],"external_id":{"arxiv":["2502.18377"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"intvolume":"       267","ec_funded":1,"page":"48962-48973","ddc":["000"],"article_processing_charge":"No","status":"public","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.","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.","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.","short":"A.A. Pervez, E. Gavves, F. Locatello, in:, 42nd International Conference on Machine Learning, ML Research Press, 2025, pp. 48962–48973.","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.","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."},"OA_type":"gold","month":"05","alternative_title":["PMLR"],"type":"conference","publication":"42nd International Conference on Machine Learning","_id":"20817","date_created":"2025-12-14T23:02:04Z","file_date_updated":"2025-12-16T12:21:49Z","conference":{"location":"Vancouver, Canada","end_date":"2025-07-19","name":"ICML: International Conference on Machine Learning","start_date":"2025-07-13"},"project":[{"grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"},{"grant_number":"COE12","name":"Bilateral Artificial Intelligence (Locatello)","_id":"a392d8f0-b034-11f1-b88e-d3025c6734f6"}],"oa":1,"day":"01","quality_controlled":"1","related_material":{"link":[{"relation":"software","url":"https://github.com/ alpz/mech-nn-discovery-pde"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Mechanistic PDE networks for discovery of governing equations"},{"OA_type":"diamond","citation":{"ama":"Pervez AA, Locatello F, Gavves E. Mechanistic neural networks for scientific machine learning. In: <i>Proceedings of the 41st International Conference on Machine Learning</i>. Vol 235. ML Research Press; 2024:40484-40501.","ista":"Pervez AA, Locatello F, Gavves E. 2024. Mechanistic neural networks for scientific machine learning. Proceedings of the 41st International Conference on Machine Learning. ICML: International Conference on Machine Learning, PMLR, vol. 235, 40484–40501.","short":"A.A. Pervez, F. Locatello, E. Gavves, in:, Proceedings of the 41st International Conference on Machine Learning, ML Research Press, 2024, pp. 40484–40501.","chicago":"Pervez, Adeel A, Francesco Locatello, and Efstratios Gavves. “Mechanistic Neural Networks for Scientific Machine Learning.” In <i>Proceedings of the 41st International Conference on Machine Learning</i>, 235:40484–501. ML Research Press, 2024.","apa":"Pervez, A. A., Locatello, F., &#38; Gavves, E. (2024). Mechanistic neural networks for scientific machine learning. In <i>Proceedings of the 41st International Conference on Machine Learning</i> (Vol. 235, pp. 40484–40501). Vienna, Austria: ML Research Press.","mla":"Pervez, Adeel A., et al. “Mechanistic Neural Networks for Scientific Machine Learning.” <i>Proceedings of the 41st International Conference on Machine Learning</i>, vol. 235, ML Research Press, 2024, pp. 40484–501.","ieee":"A. A. Pervez, F. Locatello, and E. Gavves, “Mechanistic neural networks for scientific machine learning,” in <i>Proceedings of the 41st International Conference on Machine Learning</i>, Vienna, Austria, 2024, vol. 235, pp. 40484–40501."},"status":"public","month":"09","alternative_title":["PMLR"],"type":"conference","intvolume":"       235","page":"40484-40501","article_processing_charge":"No","ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.13077"}],"title":"Mechanistic neural networks for scientific machine learning","_id":"18114","publication":"Proceedings of the 41st International Conference on Machine Learning","date_created":"2024-09-22T22:01:43Z","oa":1,"quality_controlled":"1","related_material":{"link":[{"url":"https://github.com/alpz/mech-nn","relation":"software"}]},"day":"01","conference":{"name":"ICML: International Conference on Machine Learning","location":"Vienna, Austria","end_date":"2024-07-27","start_date":"2024-07-21"},"oa_version":"Published Version","publication_identifier":{"eissn":["2640-3498"]},"author":[{"full_name":"Pervez, Adeel A","last_name":"Pervez","id":"fca6d90c-d47f-11ee-bc87-93ff51604981","first_name":"Adeel A"},{"orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco","last_name":"Locatello","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","first_name":"Francesco"},{"last_name":"Gavves","full_name":"Gavves, Efstratios","first_name":"Efstratios"}],"scopus_import":"1","OA_place":"publisher","publication_status":"published","volume":235,"year":"2024","publisher":"ML Research Press","date_updated":"2026-06-18T17:59:46Z","external_id":{"arxiv":["2402.13077"]},"abstract":[{"text":"This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential equations as representations, revealing the underlying dynamics of data and enhancing interpretability and efficiency in data modeling. Central to our approach is a novel Relaxed Linear Programming Solver (NeuRLP) inspired by a technique that reduces solving linear ODEs to solving linear programs. This integrates well with neural networks and surpasses the limitations of traditional ODE solvers enabling scalable GPU parallel processing. Overall, Mechanistic Neural Networks demonstrate their versatility for scientific machine learning applications, adeptly managing tasks from equation discovery to dynamic systems modeling. We prove their comprehensive capabilities in analyzing and interpreting complex scientific data across various applications, showing significant performance against specialized state-of-the-art methods. Source code is available at https://github.com/alpz/mech-nn.","lang":"eng"}],"department":[{"_id":"FrLo"}],"date_published":"2024-09-01T00:00:00Z","language":[{"iso":"eng"}],"arxiv":1}]