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Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes

Hostettler, Roland ; Tronarp, Filip LU and Särkkä, Simo (2018) 18th IFAC Symposium on System Identification In IFAC-PapersOnLine 51(15). p.778-783
Abstract
In this paper, we propose a Gaussian process-based nonlinear, time-varying drift model for stochastic differential equations. In particular, we combine eigenfunction expansion of the Gaussian process’ covariance kernel in the spatial input variables with spectral decomposition in the time domain to obtain a reduced rank state space representation of the drift model, which avoids the growing complexity (with respect to time) of the full Gaussian process solution. The proposed approach is evaluated on two nonlinear benchmark problems, the Bouc Wen and the cascaded tanks systems.
Please use this url to cite or link to this publication:
author
; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
host publication
18th IFAC Symposium on System Identification SYSID 2018
series title
IFAC-PapersOnLine
editor
Rojas, Christian
volume
51
issue
15
pages
778 - 783
publisher
Elsevier
conference name
18th IFAC Symposium on System Identification
conference location
Stockholm, Sweden
conference dates
2018-07-09 - 2018-07-11
external identifiers
  • scopus:85054443004
ISSN
2405-8963
2405-8971
DOI
10.1016/j.ifacol.2018.09.137
language
English
LU publication?
no
id
99964b06-fdc1-45fb-9de5-18880e62d8a6
date added to LUP
2023-08-21 02:11:48
date last changed
2024-01-19 01:15:41
@inproceedings{99964b06-fdc1-45fb-9de5-18880e62d8a6,
  abstract     = {{In this paper, we propose a Gaussian process-based nonlinear, time-varying drift model for stochastic differential equations. In particular, we combine eigenfunction expansion of the Gaussian process’ covariance kernel in the spatial input variables with spectral decomposition in the time domain to obtain a reduced rank state space representation of the drift model, which avoids the growing complexity (with respect to time) of the full Gaussian process solution. The proposed approach is evaluated on two nonlinear benchmark problems, the Bouc Wen and the cascaded tanks systems.}},
  author       = {{Hostettler, Roland and Tronarp, Filip and Särkkä, Simo}},
  booktitle    = {{18th IFAC Symposium on System Identification SYSID 2018}},
  editor       = {{Rojas, Christian}},
  issn         = {{2405-8963}},
  language     = {{eng}},
  number       = {{15}},
  pages        = {{778--783}},
  publisher    = {{Elsevier}},
  series       = {{IFAC-PapersOnLine}},
  title        = {{Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes}},
  url          = {{http://dx.doi.org/10.1016/j.ifacol.2018.09.137}},
  doi          = {{10.1016/j.ifacol.2018.09.137}},
  volume       = {{51}},
  year         = {{2018}},
}