Variational Gaussian process for optimal sensor placement

Gabor Tajnafoi; Rossella Arcucci; Laetitia Mottet; Carolanne Vouriot; Miguel Molina-Solana; Christopher Pain; Yi-Ke Guo

Applications of Mathematics (2021)

  • Volume: 66, Issue: 2, page 287-317
  • ISSN: 0862-7940

Abstract

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Sensor placement is an optimisation problem that has recently gained great relevance. In order to achieve accurate online updates of a predictive model, sensors are used to provide observations. When sensor location is optimally selected, the predictive model can greatly reduce its internal errors. A greedy-selection algorithm is used for locating these optimal spatial locations from a numerical embedded space. A novel architecture for solving this big data problem is proposed, relying on a variational Gaussian process. The generalisation of the model is further improved via the preconditioning of its inputs: Masked Autoregressive Flows are implemented to learn nonlinear, invertible transformations of the conditionally modelled spatial features. Finally, a global optimisation strategy extending the Mutual Information-based optimisation and fine-tuning of the selected optimal location is proposed. The methodology is parallelised to speed up the computational time, making these tools very fast despite the high complexity associated with both spatial modelling and placement tasks. The model is applied to a real three-dimensional test case considering a room within the Clarence Centre building located in Elephant and Castle, London, UK.

How to cite

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Tajnafoi, Gabor, et al. "Variational Gaussian process for optimal sensor placement." Applications of Mathematics 66.2 (2021): 287-317. <http://eudml.org/doc/297705>.

@article{Tajnafoi2021,
abstract = {Sensor placement is an optimisation problem that has recently gained great relevance. In order to achieve accurate online updates of a predictive model, sensors are used to provide observations. When sensor location is optimally selected, the predictive model can greatly reduce its internal errors. A greedy-selection algorithm is used for locating these optimal spatial locations from a numerical embedded space. A novel architecture for solving this big data problem is proposed, relying on a variational Gaussian process. The generalisation of the model is further improved via the preconditioning of its inputs: Masked Autoregressive Flows are implemented to learn nonlinear, invertible transformations of the conditionally modelled spatial features. Finally, a global optimisation strategy extending the Mutual Information-based optimisation and fine-tuning of the selected optimal location is proposed. The methodology is parallelised to speed up the computational time, making these tools very fast despite the high complexity associated with both spatial modelling and placement tasks. The model is applied to a real three-dimensional test case considering a room within the Clarence Centre building located in Elephant and Castle, London, UK.},
author = {Tajnafoi, Gabor, Arcucci, Rossella, Mottet, Laetitia, Vouriot, Carolanne, Molina-Solana, Miguel, Pain, Christopher, Guo, Yi-Ke},
journal = {Applications of Mathematics},
keywords = {sensor placement; variational Gaussian process; mutual information},
language = {eng},
number = {2},
pages = {287-317},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variational Gaussian process for optimal sensor placement},
url = {http://eudml.org/doc/297705},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Tajnafoi, Gabor
AU - Arcucci, Rossella
AU - Mottet, Laetitia
AU - Vouriot, Carolanne
AU - Molina-Solana, Miguel
AU - Pain, Christopher
AU - Guo, Yi-Ke
TI - Variational Gaussian process for optimal sensor placement
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 287
EP - 317
AB - Sensor placement is an optimisation problem that has recently gained great relevance. In order to achieve accurate online updates of a predictive model, sensors are used to provide observations. When sensor location is optimally selected, the predictive model can greatly reduce its internal errors. A greedy-selection algorithm is used for locating these optimal spatial locations from a numerical embedded space. A novel architecture for solving this big data problem is proposed, relying on a variational Gaussian process. The generalisation of the model is further improved via the preconditioning of its inputs: Masked Autoregressive Flows are implemented to learn nonlinear, invertible transformations of the conditionally modelled spatial features. Finally, a global optimisation strategy extending the Mutual Information-based optimisation and fine-tuning of the selected optimal location is proposed. The methodology is parallelised to speed up the computational time, making these tools very fast despite the high complexity associated with both spatial modelling and placement tasks. The model is applied to a real three-dimensional test case considering a room within the Clarence Centre building located in Elephant and Castle, London, UK.
LA - eng
KW - sensor placement; variational Gaussian process; mutual information
UR - http://eudml.org/doc/297705
ER -

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