Applications of Mathematics, Vol. 66, No. 2, pp. 287-317, 2021

Variational Gaussian process for optimal sensor placement

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

Received November 16, 2019.   Published online February 12, 2021.

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.
Keywords:  sensor placement; variational Gaussian process; mutual information
Classification MSC:  65Z05, 68T99
DOI:  10.21136/AM.2021.0307-19

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Affiliations:   Gabor Tajnafoi, Rossella Arcucci (corresponding author), Data Science Institute, Department of Computing, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom, e-mail:,,; Laetitia Mottet, Applied Modelling and Computation Group, Department of Earth Science & Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom, e-mail:; Carolanne Vouriot, Department of Civil Engineering, Imperial College London, 58 Princes Gate, Kensington, London SW7 1AL, United Kigdom, e-mail:; Miguel Molina-Solana, Department of Computer Science and AI, Universidad de Granada, 18071 Granada, Spain, and Data Science Institute, Department of Computing, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom, e-mail:; Christopher Pain, Department of Earth Science & Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom, e-mail:; Yi-Ke Guo, Data Science Institute, Department of Computing, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom, e-mail:

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