Pick-and-mix information operators for probabilistic ODE solvers
(2022) 25th International Conference on Artificial Intelligence and Statistics In Proceedings of Machine Learning Research 151.- Abstract
- Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference. In this paper, we leverage their probabilistic formulation to seamlessly include additional information as general likelihood terms. We show that second-order differential equations should be directly provided to the solver, instead of transforming the problem to first order. Additionally, by including higher-order information or physical conservation laws in the model, solutions become more accurate and more physically meaningful. Lastly, we demonstrate the utility of flexible information operators by solving differential-algebraic equations. In conclusion, the... (More)
- Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference. In this paper, we leverage their probabilistic formulation to seamlessly include additional information as general likelihood terms. We show that second-order differential equations should be directly provided to the solver, instead of transforming the problem to first order. Additionally, by including higher-order information or physical conservation laws in the model, solutions become more accurate and more physically meaningful. Lastly, we demonstrate the utility of flexible information operators by solving differential-algebraic equations. In conclusion, the probabilistic formulation of numerical solvers offers a flexible way to incorporate various types of information, thus improving the resulting solutions. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4e4a059c-b922-48f0-b013-5c658a71fea6
- author
- Bosch, Nathanael ; Tronarp, Filip LU and Hennig, Philipp
- publishing date
- 2022
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of The 25th International Conference on Artificial Intelligence and Statistics
- series title
- Proceedings of Machine Learning Research
- volume
- 151
- publisher
- ML Research Press
- conference name
- 25th International Conference on Artificial Intelligence and Statistics
- conference location
- Virtual
- conference dates
- 2022-03-28 - 2022-03-30
- external identifiers
-
- scopus:85162129254
- ISSN
- 2640-3498
- language
- English
- LU publication?
- no
- id
- 4e4a059c-b922-48f0-b013-5c658a71fea6
- alternative location
- https://proceedings.mlr.press/v151/bosch22a.html
- date added to LUP
- 2023-08-20 22:56:30
- date last changed
- 2024-02-28 08:55:34
@inproceedings{4e4a059c-b922-48f0-b013-5c658a71fea6,
abstract = {{Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference. In this paper, we leverage their probabilistic formulation to seamlessly include additional information as general likelihood terms. We show that second-order differential equations should be directly provided to the solver, instead of transforming the problem to first order. Additionally, by including higher-order information or physical conservation laws in the model, solutions become more accurate and more physically meaningful. Lastly, we demonstrate the utility of flexible information operators by solving differential-algebraic equations. In conclusion, the probabilistic formulation of numerical solvers offers a flexible way to incorporate various types of information, thus improving the resulting solutions.}},
author = {{Bosch, Nathanael and Tronarp, Filip and Hennig, Philipp}},
booktitle = {{Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}},
issn = {{2640-3498}},
language = {{eng}},
publisher = {{ML Research Press}},
series = {{Proceedings of Machine Learning Research}},
title = {{Pick-and-mix information operators for probabilistic ODE solvers}},
url = {{https://proceedings.mlr.press/v151/bosch22a.html}},
volume = {{151}},
year = {{2022}},
}