Environmental sensors are crucial for monitoring weather conditions and the impacts of climate change. However, it is challenging to place sensors in a way that maximises the informativeness of their measurements, particularly in remote regions like Antarctica. Probabilistic machine learning models can suggest informative sensor placements by finding sites that maximally reduce prediction uncertainty. Gaussian process (GP) models are widely used for this purpose, but they struggle with capturing complex non-stationary behaviour and scaling to large datasets. This paper proposes using a convolutional Gaussian neural process (ConvGNP) to address these issues. A ConvGNP uses neural networks to parameterise a joint Gaussian distribution at arbitrary target locations, enabling flexibility and scalability. Using simulated surface air temperature anomaly over Antarctica as training data, the ConvGNP learns spatial and seasonal non-stationarities, outperforming a non-stationary GP baseline. In a simulated sensor placement experiment, the ConvGNP better predicts the performance boost obtained from new observations than GP baselines, leading to more informative sensor placements. We contrast our approach with physics-based sensor placement methods and propose future steps towards an operational sensor placement recommendation system. Our work could help to realise environmental digital twins that actively direct measurement sampling to improve the digital representation of reality.

This paper considers the placement of m sensors at n > m possible locations. Given noisy observations, knowledge of the state correlation matrix, and a mean-square error criterion (equivalently maximizing an efficacy cost criterion), the problem is formulated as an integer programming problem. Computing the solution for large m and n is infeasible, requiring us to look at approximate algorithms and bounding optimal performance. Approximate algorithms include greedy algorithms and variations based on examining the efficacy cost function and projection-based methods that all run in polynomial time of m and n. A sequence of nested bounds are found that upper bound the optimal performance (with analysis based on using matrix pencils and generalized eigenvectors). Finally, we show through simulations that the approximate algorithms perform well and provide tight implementable lower bounds to optimal performance and the nested bounds provide upper bounds to optimal performance with tighter bounds achieved with increasing complexity. The sensor placement problem has many energy applications where we are often confronted with limited resources. Some examples include where to place environmental sensors for an area in which there are many distributed solar photovoltaic generators and where to place grid monitors on an electrical distribution microgrid.