---
_id: '12804'
abstract:
- lang: eng
text: 'Data in many applications follows systems of Ordinary Differential Equations
(ODEs). This paper presents a novel algorithmic and symbolic construction for
covariance functions of Gaussian Processes (GPs) with realizations strictly following
a system of linear homogeneous ODEs with constant coefficients, which we call
LODE-GPs. Introducing this strong inductive bias into a GP improves modelling
of such data. Using smith normal form algorithms, a symbolic technique, we overcome
two current restrictions in the state of the art: (1) the need for certain uniqueness
conditions in the set of solutions, typically assumed in classical ODE solvers
and their probabilistic counterparts, and (2) the restriction to controllable
systems, typically assumed when encoding differential equations in covariance
functions. We show the effectiveness of LODE-GPs in a number of experiments, for
example learning physically interpretable parameters by maximizing the likelihood.'
author:
- first_name: Andreas
full_name: Besginow, Andreas
id: '61743'
last_name: Besginow
- first_name: Markus
full_name: Lange-Hegermann, Markus
id: '71761'
last_name: Lange-Hegermann
citation:
ama: Besginow A, Lange-Hegermann M. Constraining Gaussian Processes to Systems
of Linear Ordinary Differential Equations. Vol 35. (Koyejo S, Mohamed S, Agarwal
A, et al., eds.). Curran Associates, Inc.; 2022:29386-29399.
apa: Besginow, A., & Lange-Hegermann, M. (2022). Constraining Gaussian Processes
to Systems of Linear Ordinary Differential Equations. In S. Koyejo, S. Mohamed,
A. Agarwal, D. Belgrave, K. Cho, A. Oh, & Neural Information Processing Systems
Foundation (Eds.), 36th Conference on Neural Information Processing Systems
(NeurIPS 2022) (Vol. 35, pp. 29386–29399). Curran Associates, Inc.
bjps: 'Besginow A and Lange-Hegermann M (2022) Constraining Gaussian Processes
to Systems of Linear Ordinary Differential Equations, Koyejo S et al. (eds).
Red Hook, NY : Curran Associates, Inc.'
chicago: 'Besginow, Andreas, and Markus Lange-Hegermann. Constraining Gaussian
Processes to Systems of Linear Ordinary Differential Equations. Edited by
S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh, and Neural Information
Processing Systems Foundation . 36th Conference on Neural Information Processing
Systems (NeurIPS 2022) . Vol. 35. Advances in Neural Information Processing
Systems. Red Hook, NY : Curran Associates, Inc., 2022.'
chicago-de: 'Besginow, Andreas und Markus Lange-Hegermann. 2022. Constraining
Gaussian Processes to Systems of Linear Ordinary Differential Equations. Hg.
von S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh, und Neural
Information Processing Systems Foundation . 36th Conference on Neural Information
Processing Systems (NeurIPS 2022) . Bd. 35. Advances in Neural Information
Processing Systems. Red Hook, NY : Curran Associates, Inc.'
din1505-2-1: 'Besginow, Andreas ;
Lange-Hegermann, Markus ; Koyejo, S. ; Mohamed,
S. ; Agarwal, A. ; Belgrave, D. ; Cho,
K. ; Oh, A. ; Neural
Information Processing Systems Foundation (Hrsg.): Constraining Gaussian
Processes to Systems of Linear Ordinary Differential Equations, Advances
in Neural Information Processing Systems. Bd. 35. Red Hook, NY : Curran Associates,
Inc., 2022'
havard: A. Besginow, M. Lange-Hegermann, Constraining Gaussian Processes to Systems
of Linear Ordinary Differential Equations, Curran Associates, Inc., Red Hook,
NY , 2022.
ieee: 'A. Besginow and M. Lange-Hegermann, Constraining Gaussian Processes to
Systems of Linear Ordinary Differential Equations, vol. 35. Red Hook, NY :
Curran Associates, Inc., 2022, pp. 29386–29399.'
mla: Besginow, Andreas, and Markus Lange-Hegermann. “Constraining Gaussian Processes
to Systems of Linear Ordinary Differential Equations.” 36th Conference on Neural
Information Processing Systems (NeurIPS 2022) , edited by S. Koyejo et al.,
vol. 35, Curran Associates, Inc., 2022, pp. 29386–99.
short: A. Besginow, M. Lange-Hegermann, Constraining Gaussian Processes to Systems
of Linear Ordinary Differential Equations, Curran Associates, Inc., Red Hook,
NY , 2022.
ufg: 'Besginow, Andreas/Lange-Hegermann, Markus: Constraining Gaussian Processes
to Systems of Linear Ordinary Differential Equations, Bd. 35, hg. von Koyejo,
S. u. a., Red Hook, NY 2022 (Advances in Neural Information Processing Systems).'
van: 'Besginow A, Lange-Hegermann M. Constraining Gaussian Processes to Systems
of Linear Ordinary Differential Equations. Koyejo S, Mohamed S, Agarwal A, Belgrave
D, Cho K, Oh A, et al., editors. 36th Conference on Neural Information Processing
Systems (NeurIPS 2022) . Red Hook, NY : Curran Associates, Inc.; 2022. (Advances
in Neural Information Processing Systems; vol. 35).'
conference:
end_date: 2022-12-09
location: New Orleans, La.; Online
name: 36th Conference on Neural Information Processing Systems (NeurIPS)
start_date: 2022-11-28
corporate_editor:
- 'Neural Information Processing Systems Foundation '
date_created: 2025-04-16T06:58:04Z
date_updated: 2025-06-26T13:37:53Z
department:
- _id: DEP5000
editor:
- first_name: S.
full_name: Koyejo, S.
last_name: Koyejo
- first_name: S.
full_name: Mohamed, S.
last_name: Mohamed
- first_name: A.
full_name: Agarwal, A.
last_name: Agarwal
- first_name: D.
full_name: Belgrave, D.
last_name: Belgrave
- first_name: K.
full_name: Cho, K.
last_name: Cho
- first_name: A.
full_name: Oh, A.
last_name: Oh
intvolume: ' 35'
keyword:
- SMITH NORMAL-FORM
- ALGORITHMS
- REDUCTION
language:
- iso: eng
page: 29386 - 29399
place: 'Red Hook, NY '
publication: '36th Conference on Neural Information Processing Systems (NeurIPS 2022) '
publication_identifier:
eisbn:
- 978-1-7138-7312-9
isbn:
- '978-1-7138-7108-8 '
issn:
- 1049-5258
publication_status: published
publisher: Curran Associates, Inc.
series_title: Advances in Neural Information Processing Systems
status: public
title: Constraining Gaussian Processes to Systems of Linear Ordinary Differential
Equations
type: conference_editor_article
user_id: '83781'
volume: 35
year: '2022'
...