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Fenrir: Physics-Enhanced Regression for Initial Value Problems

Tronarp, Filip LU ; Hennig, Philipp and Bosch, Nathanael (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)
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author
; and
publishing date
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}},
}