{"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/machine-learning-of-linear-differential","title":"Machine Learning of Linear Differential Equations using Gaussian Processes","arxiv_id":"1701.02440","date":"2017-01-10","proceeding":null,"authors":["Maziar Raissi","George Em. Karniadakis"],"abstract":"This work leverages recent advances in probabilistic machine learning to\ndiscover conservation laws expressed by parametric linear equations. Such\nequations involve, but are not limited to, ordinary and partial differential,\nintegro-differential, and fractional order operators. Here, Gaussian process\npriors are modified according to the particular form of such operators and are\nemployed to infer parameters of the linear equations from scarce and possibly\nnoisy observations. Such observations may come from experiments or \"black-box\"\ncomputer simulations.","url_abs":"http://arxiv.org/abs/1701.02440v1","url_pdf":"http://arxiv.org/pdf/1701.02440v1.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":"machine-learning-of-linear-differential","repo_url":"https://github.com/Slowpuncher24/mlhiphy_v2","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"machine-learning-of-linear-differential","repo_url":"https://github.com/maziarraissi/TutorialGP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1701.02440","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}