Calibrated Adaptive Probabilistic ODE Solvers
(2021) 24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 In Proceedings of Machine Learning Research 130. p.3466-3474- Abstract
Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error, but its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error. Addressing this issue, we introduce, discuss, and assess several probabilistically motivated ways to calibrate the uncertainty estimate. Numerical experiments demonstrate that these calibration methods interact efficiently with adaptive step-size selection,... (More)
Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error, but its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error. Addressing this issue, we introduce, discuss, and assess several probabilistically motivated ways to calibrate the uncertainty estimate. Numerical experiments demonstrate that these calibration methods interact efficiently with adaptive step-size selection, resulting in descriptive, and efficiently computable posteriors. We demonstrate the efficiency of the methodology by benchmarking against the classic, widely used Dormand-Prince 4/5 Runge-Kutta method.
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- author
- Bosch, Nathanael ; Hennig, Philipp and Tronarp, Filip LU
- publishing date
- 2021
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- International Conference on Artificial Intelligence and Statistics
- series title
- Proceedings of Machine Learning Research
- volume
- 130
- pages
- 9 pages
- publisher
- ML Research Press
- conference name
- 24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021
- conference location
- Virtual, Online, United States
- conference dates
- 2021-04-13 - 2021-04-15
- external identifiers
-
- scopus:85119141008
- ISSN
- 2640-3498
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: Copyright © 2021 by the author(s)
- id
- 49c80d5f-dc1a-4f4c-b388-d3872dcffe3a
- alternative location
- https://proceedings.mlr.press/v130/bosch21a.html
- date added to LUP
- 2023-08-23 15:49:13
- date last changed
- 2025-04-04 15:07:17
@inproceedings{49c80d5f-dc1a-4f4c-b388-d3872dcffe3a,
abstract = {{<p>Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error, but its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error. Addressing this issue, we introduce, discuss, and assess several probabilistically motivated ways to calibrate the uncertainty estimate. Numerical experiments demonstrate that these calibration methods interact efficiently with adaptive step-size selection, resulting in descriptive, and efficiently computable posteriors. We demonstrate the efficiency of the methodology by benchmarking against the classic, widely used Dormand-Prince 4/5 Runge-Kutta method.</p>}},
author = {{Bosch, Nathanael and Hennig, Philipp and Tronarp, Filip}},
booktitle = {{International Conference on Artificial Intelligence and Statistics}},
issn = {{2640-3498}},
language = {{eng}},
pages = {{3466--3474}},
publisher = {{ML Research Press}},
series = {{Proceedings of Machine Learning Research}},
title = {{Calibrated Adaptive Probabilistic ODE Solvers}},
url = {{https://proceedings.mlr.press/v130/bosch21a.html}},
volume = {{130}},
year = {{2021}},
}