{"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/learning-unknown-ode-models-with-gaussian","title":"Learning unknown ODE models with Gaussian processes","arxiv_id":"1803.04303","date":"2018-03-12","proceeding":"ICML 2018 7","authors":["Markus Heinonen","Cagatay Yildiz","Henrik Mannerström","Jukka Intosalmi","Harri Lähdesmäki"],"abstract":"In conventional ODE modelling coefficients of an equation driving the system\nstate forward in time are estimated. However, for many complex systems it is\npractically impossible to determine the equations or interactions governing the\nunderlying dynamics. In these settings, parametric ODE model cannot be\nformulated. Here, we overcome this issue by introducing a novel paradigm of\nnonparametric ODE modelling that can learn the underlying dynamics of arbitrary\ncontinuous-time systems without prior knowledge. We propose to learn\nnon-linear, unknown differential functions from state observations using\nGaussian process vector fields within the exact ODE formalism. We demonstrate\nthe model's capabilities to infer dynamics from sparse data and to simulate the\nsystem forward into future.","url_abs":"http://arxiv.org/abs/1803.04303v1","url_pdf":"http://arxiv.org/pdf/1803.04303v1.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":"learning-unknown-ode-models-with-gaussian","repo_url":"https://github.com/cagatayyildiz/npode","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"learning-unknown-ode-models-with-gaussian","repo_url":"https://github.com/cagatayyildiz/npde","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1803.04303","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}