{"ddc":["000"],"status":"public","year":"2025","_id":"20592","alternative_title":["PMLR"],"arxiv":1,"date_published":"2025-01-01T00:00:00Z","department":[{"_id":"FrLo"}],"publication_status":"published","day":"01","volume":271,"publication":"Proceedings of the 1st International Conference on Probabilistic Numerics","intvolume":"       271","acknowledgement":"NB gratefully acknowledge co-funding by the European Union (ERC, ANUBIS, 101123955. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them). NB thanks the International\r\nMax Planck Research School for Intelligent Systems (IMPRS-IS) for their support.","citation":{"ista":"Yao D, Tronarp F, Bosch N. 2025. Propagating model uncertainty through filtering-based probabilistic numerical ODE solvers. Proceedings of the 1st International Conference on Probabilistic Numerics. ProbNum: Conference on Probabilistic Numerics, PMLR, vol. 271.","ama":"Yao D, Tronarp F, Bosch N. Propagating model uncertainty through filtering-based probabilistic numerical ODE solvers. In: <i>Proceedings of the 1st International Conference on Probabilistic Numerics</i>. Vol 271. ML Research Press; 2025.","mla":"Yao, Dingling, et al. “Propagating Model Uncertainty through Filtering-Based Probabilistic Numerical ODE Solvers.” <i>Proceedings of the 1st International Conference on Probabilistic Numerics</i>, vol. 271, ML Research Press, 2025.","ieee":"D. Yao, F. Tronarp, and N. Bosch, “Propagating model uncertainty through filtering-based probabilistic numerical ODE solvers,” in <i>Proceedings of the 1st International Conference on Probabilistic Numerics</i>, Sophia Antipolis, France, 2025, vol. 271.","short":"D. Yao, F. Tronarp, N. Bosch, in:, Proceedings of the 1st International Conference on Probabilistic Numerics, ML Research Press, 2025.","apa":"Yao, D., Tronarp, F., &#38; Bosch, N. (2025). Propagating model uncertainty through filtering-based probabilistic numerical ODE solvers. In <i>Proceedings of the 1st International Conference on Probabilistic Numerics</i> (Vol. 271). Sophia Antipolis, France: ML Research Press.","chicago":"Yao, Dingling, Filip Tronarp, and Nathanael Bosch. “Propagating Model Uncertainty through Filtering-Based Probabilistic Numerical ODE Solvers.” In <i>Proceedings of the 1st International Conference on Probabilistic Numerics</i>, Vol. 271. ML Research Press, 2025."},"publication_identifier":{"eissn":["2640-3498"]},"article_processing_charge":"No","oa_version":"Preprint","type":"conference","language":[{"iso":"eng"}],"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png"},"quality_controlled":"1","month":"01","title":"Propagating model uncertainty through filtering-based probabilistic numerical ODE solvers","scopus_import":"1","conference":{"name":"ProbNum: Conference on Probabilistic Numerics","start_date":"2025-09-01","end_date":"2025-09-03","location":"Sophia Antipolis, France"},"date_updated":"2025-11-10T08:33:11Z","OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2025-11-02T23:01:35Z","author":[{"last_name":"Yao","full_name":"Yao, Dingling","id":"d3e02e50-48a8-11ee-8f62-c108061797fa","first_name":"Dingling"},{"full_name":"Tronarp, Filip","last_name":"Tronarp","first_name":"Filip"},{"first_name":"Nathanael","last_name":"Bosch","full_name":"Bosch, Nathanael"}],"publisher":"ML Research Press","OA_type":"green","abstract":[{"lang":"eng","text":"Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs), also known as ODE filters, have been established as efficient methods for quantifying numerical uncertainty in the solution of ODEs. In practical applications, however, the underlying dynamical system often contains uncertain parameters, requiring the propagation of this model uncertainty to the ODE solution. In this paper, we demonstrate that ODE filters, despite their probabilistic nature, do not automatically solve this uncertainty propagation problem. To address this limitation, we present a novel approach that combines ODE filters with numerical quadrature to properly marginalize over uncertain parameters, while accounting for both parameter uncertainty and numerical solver uncertainty. Experiments across multiple dynamical systems demonstrate that the resulting uncertainty estimates closely match reference solutions. Notably, we show\r\nhow the numerical uncertainty from the ODE solver can help prevent overconfidence in the propagated uncertainty estimates, especially when using larger step sizes. Our results illustrate that probabilistic numerical methods can effectively quantify both numerical and parametric uncertainty in dynamical systems. "}],"external_id":{"arxiv":["2503.04684"]},"has_accepted_license":"1","license":"https://creativecommons.org/licenses/by-sa/4.0/","main_file_link":[{"open_access":"1","url":"https://openreview.net/forum?id=sgPCP9jOlS"}]}