Propagating Model Uncertainty through Filtering-based Probabilistic Numerical ODE Solvers
(2025) 1st International Conference on Probabilistic Numerics, ProbNum 2025 In Proceedings of Machine Learning Research 271.- Abstract
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... (More)
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 how 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.
(Less)
- author
- Yao, Dingling ; Tronarp, Filip LU and Bosch, Nathanael
- organization
- publishing date
- 2025
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of Machine Learning Research
- series title
- Proceedings of Machine Learning Research
- volume
- 271
- conference name
- 1st International Conference on Probabilistic Numerics, ProbNum 2025
- conference location
- Sophia Antipolis, France
- conference dates
- 2025-09-01 - 2025-09-03
- external identifiers
-
- scopus:105019982549
- ISSN
- 2640-3498
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2025 with the author(s).
- id
- 87b6f789-2e94-4074-93c3-a13fd02793d2
- date added to LUP
- 2026-01-15 12:48:04
- date last changed
- 2026-01-15 12:49:10
@inproceedings{87b6f789-2e94-4074-93c3-a13fd02793d2,
abstract = {{<p>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 how 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.</p>}},
author = {{Yao, Dingling and Tronarp, Filip and Bosch, Nathanael}},
booktitle = {{Proceedings of Machine Learning Research}},
issn = {{2640-3498}},
language = {{eng}},
series = {{Proceedings of Machine Learning Research}},
title = {{Propagating Model Uncertainty through Filtering-based Probabilistic Numerical ODE Solvers}},
volume = {{271}},
year = {{2025}},
}