{"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/data-driven-discovery-of-pdes-in-complex","title":"Data-driven discovery of PDEs in complex datasets","arxiv_id":"1808.10788","date":"2018-08-31","proceeding":null,"authors":["Jens Berg","Kaj Nyström"],"abstract":"Many processes in science and engineering can be described by partial\ndifferential equations (PDEs). Traditionally, PDEs are derived by considering\nfirst principles of physics to derive the relations between the involved\nphysical quantities of interest. A different approach is to measure the\nquantities of interest and use deep learning to reverse engineer the PDEs which\nare describing the physical process.\n  In this paper we use machine learning, and deep learning in particular, to\ndiscover PDEs hidden in complex data sets from measurement data. We include\nexamples of data from a known model problem, and real data from weather station\nmeasurements. We show how necessary transformations of the input data amounts\nto coordinate transformations in the discovered PDE, and we elaborate on\nfeature and model selection. It is shown that the dynamics of a non-linear,\nsecond order PDE can be accurately described by an ordinary differential\nequation which is automatically discovered by our deep learning algorithm. Even\nmore interestingly, we show that similar results apply in the context of more\ncomplex simulations of the Swedish temperature distribution.","url_abs":"http://arxiv.org/abs/1808.10788v1","url_pdf":"http://arxiv.org/pdf/1808.10788v1.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":"data-driven-discovery-of-pdes-in-complex","repo_url":"https://github.com/arnauldnzegha/deep2pde_Berg_Nystrom","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"model-selection","task_name":"Model Selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}