Fenrir: Physics-Enhanced Regression for Initial Value Problems

Filip Tronarp, Nathanael Bosch, Philipp Hennig
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:21776-21794, 2022.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-tronarp22a, title = {Fenrir: Physics-Enhanced Regression for Initial Value Problems}, author = {Tronarp, Filip and Bosch, Nathanael and Hennig, Philipp}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {21776--21794}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/tronarp22a/tronarp22a.pdf}, url = {https://proceedings.mlr.press/v162/tronarp22a.html}, 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.} }
Endnote
%0 Conference Paper %T Fenrir: Physics-Enhanced Regression for Initial Value Problems %A Filip Tronarp %A Nathanael Bosch %A Philipp Hennig %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-tronarp22a %I PMLR %P 21776--21794 %U https://proceedings.mlr.press/v162/tronarp22a.html %V 162 %X 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.
APA
Tronarp, F., Bosch, N. & Hennig, P.. (2022). Fenrir: Physics-Enhanced Regression for Initial Value Problems. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:21776-21794 Available from https://proceedings.mlr.press/v162/tronarp22a.html.

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