{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/modalpinn-an-extension-of-physics-informed","title":"ModalPINN: an extension of Physics-Informed Neural Networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors","arxiv_id":"2108.08929","date":"2021-08-19","proceeding":null,"authors":["Gaetan Raynaud","Sebastien Houde","Frederick P. Gosselin"],"abstract":"Continuous reconstructions of periodic phenomena provide powerful tools to understand, predict and model natural situations and engineering problems. In line with the recent method called Physics-Informed Neural Networks (PINN) where a multi layer perceptron directly approximates any physical quantity as a symbolic function of time and space coordinates, we present an extension, namely ModalPINN, that encodes the approximation of a limited number of Fourier mode shapes. In addition to the added interpretability, this representation performs up to two orders of magnitude more precisely for a similar number of degrees of freedom and training time in some cases as illustrated through the test case of laminar shedding of vortices over a cylinder. This added simplicity proves to be robust in regards to flow reconstruction using only a limited number of sensors with asymmetric data that simulates an experimental configuration, even when a Gaussian noise or a random delay is added, imitating imperfect and sparse information.","url_abs":"https://arxiv.org/abs/2108.08929v3","url_pdf":"https://arxiv.org/pdf/2108.08929v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"modalpinn-an-extension-of-physics-informed","repo_url":"https://github.com/GRaynaud/ModalPINN_Python_code","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}