{"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/pde-learn-using-deep-learning-to-discover","title":"PDE-LEARN: Using Deep Learning to Discover Partial Differential Equations from Noisy, Limited Data","arxiv_id":"2212.04971","date":"2022-12-09","proceeding":null,"authors":["Robert Stephany","Christopher Earls"],"abstract":"In this paper, we introduce PDE-LEARN, a novel deep learning algorithm that can identify governing partial differential equations (PDEs) directly from noisy, limited measurements of a physical system of interest. PDE-LEARN uses a Rational Neural Network, $U$, to approximate the system response function and a sparse, trainable vector, $\\xi$, to characterize the hidden PDE that the system response function satisfies. Our approach couples the training of $U$ and $\\xi$ using a loss function that (1) makes $U$ approximate the system response function, (2) encapsulates the fact that $U$ satisfies a hidden PDE that $\\xi$ characterizes, and (3) promotes sparsity in $\\xi$ using ideas from iteratively reweighted least-squares. Further, PDE-LEARN can simultaneously learn from several data sets, allowing it to incorporate results from multiple experiments. This approach yields a robust algorithm to discover PDEs directly from realistic scientific data. We demonstrate the efficacy of PDE-LEARN by identifying several PDEs from noisy and limited measurements.","url_abs":"https://arxiv.org/abs/2212.04971v2","url_pdf":"https://arxiv.org/pdf/2212.04971v2.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":"pde-learn-using-deep-learning-to-discover","repo_url":"https://github.com/punkduckable/pde-learn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","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}