Fenrir: Physics-Enhanced Regression for Initial Value Problems
(2022) 39th International Conference on Machine Learning, ICML 2022 In Proceedings of Machine Learning Research 162.- Abstract
- We show how probabilistic numerics can be used to convert an initial value problem into a Gauss–Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary differential equations is reduced to hyper-parameter estimation in Gauss–Markov regression, which tends to be considerably easier. The method’s relation and benefits in comparison to classical numerical integration and gradient matching approaches is elucidated. In particular, the method can, in contrast to gradient matching, handle partial observations, and has certain routes for escaping local optima not available to classical numerical integration. Experimental results demonstrate that the... (More)
- We show how probabilistic numerics can be used to convert an initial value problem into a Gauss–Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary differential equations is reduced to hyper-parameter estimation in Gauss–Markov regression, which tends to be considerably easier. The method’s relation and benefits in comparison to classical numerical integration and gradient matching approaches is elucidated. In particular, the method can, in contrast to gradient matching, handle partial observations, and has certain routes for escaping local optima not available to classical numerical integration. Experimental results demonstrate that the method is on par or moderately better than competing approaches. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/e14acedb-1375-4eb3-9a79-f70211fe7c82
- author
- Tronarp, Filip LU ; Hennig, Philipp and Bosch, Nathanael
- publishing date
- 2022
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the 39th International Conference on Machine Learning
- series title
- Proceedings of Machine Learning Research
- volume
- 162
- publisher
- ML Research Press
- conference name
- 39th International Conference on Machine Learning, ICML 2022
- conference location
- Baltimore, United States
- conference dates
- 2022-07-17 - 2022-07-23
- external identifiers
-
- scopus:85147406656
- ISSN
- 2640-3498
- language
- English
- LU publication?
- no
- id
- e14acedb-1375-4eb3-9a79-f70211fe7c82
- alternative location
- https://proceedings.mlr.press/v162/tronarp22a.html
- date added to LUP
- 2023-08-20 22:52:56
- date last changed
- 2024-01-22 04:04:45
@inproceedings{e14acedb-1375-4eb3-9a79-f70211fe7c82, abstract = {{We show how probabilistic numerics can be used to convert an initial value problem into a Gauss–Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary differential equations is reduced to hyper-parameter estimation in Gauss–Markov regression, which tends to be considerably easier. The method’s relation and benefits in comparison to classical numerical integration and gradient matching approaches is elucidated. In particular, the method can, in contrast to gradient matching, handle partial observations, and has certain routes for escaping local optima not available to classical numerical integration. Experimental results demonstrate that the method is on par or moderately better than competing approaches.}}, author = {{Tronarp, Filip and Hennig, Philipp and Bosch, Nathanael}}, booktitle = {{Proceedings of the 39th International Conference on Machine Learning}}, issn = {{2640-3498}}, language = {{eng}}, publisher = {{ML Research Press}}, series = {{Proceedings of Machine Learning Research}}, title = {{Fenrir: Physics-Enhanced Regression for Initial Value Problems}}, url = {{https://proceedings.mlr.press/v162/tronarp22a.html}}, volume = {{162}}, year = {{2022}}, }