{"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/weak-pde-learn-a-weak-form-based-approach-to","title":"Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data","arxiv_id":"2309.04699","date":"2023-09-09","proceeding":null,"authors":["Robert Stephany","Christopher Earls"],"abstract":"We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. Weak-PDE-LEARN uses an adaptive loss function based on weak forms to train a neural network, $U$, to approximate the PDE solution while simultaneously identifying the governing PDE. This approach yields an algorithm that is robust to noise and can discover a range of PDEs directly from noisy, limited measurements of their solutions. We demonstrate the efficacy of Weak-PDE-LEARN by learning several benchmark PDEs.","url_abs":"https://arxiv.org/abs/2309.04699v1","url_pdf":"https://arxiv.org/pdf/2309.04699v1.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":"abstracts"},"code_links":[{"paper_slug":"weak-pde-learn-a-weak-form-based-approach-to","repo_url":"https://github.com/punkduckable/weak_pde_learn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"form","task_name":"Form"}],"methods":[{"method_slug":"adaptive-loss","method_name":"Adaptive Loss"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}