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Gahungu, P., Lanyon, C.W., Álvarez, M.A. et al. (3 more authors) (2022) Adjoint-aided inference of Gaussian process driven differential equations. In: Advances in Neural Information Processing Systems (NeurIPS 2022). 36th Conference on Neural Information Processing Systems (NeurIPS 2022), 28 Nov - 09 Dec 2022, New Orleans, LA, USA. ISBN 9781713871088
Abstract
Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the forcing, as well as other unknown parameters. In differential equations, the forcing function is an unknown function of the independent variables (typically time and space), and can be modelled as a Gaussian process (GP). In this paper we show how the adjoint of a linear system can be used to efficiently infer forcing functions modelled as GPs, using a truncated basis expansion of the GP kernel. We show how exact conjugate Bayesian inference for the truncated GP can be achieved, in many cases with substantially lower computation than would be required using MCMC methods. We demonstrate the approach on systems of both ordinary and partial differential equations, and show that the basis expansion approach approximates well the true forcing with a modest number of basis vectors. Finally, we show how to infer point estimates for the non-linear model parameters, such as the kernel length-scales, using Bayesian optimisation.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Authors. This is an author produced version of a paper subsequently published in Advances in Neural Information Processing Systems (NeurIPS 2022). Available under a Creative Commons Attribution 4.0 International License. (https://creativecommons.org/licenses/by/4.0/) |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Funding Information: | Funder Grant number GOOGLE.ORG Google AirQo Project ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/T00343X/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 25 Aug 2023 09:52 |
Last Modified: | 25 Aug 2023 10:46 |
Published Version: | https://proceedings.neurips.cc/paper_files/paper/2... |
Status: | Published |
Refereed: | Yes |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:202658 |
Available Versions of this Item
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Adjoint-aided inference of Gaussian process driven differential equations. (deposited 25 Aug 2023 09:40)
- Adjoint-aided inference of Gaussian process driven differential equations. (deposited 25 Aug 2023 09:52) [Currently Displayed]