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We propose a new approach to the optimal placement of sensors for the problemof reconstructing geophysical fields from sparse measurements. Our methodconsists of two stages. In the first stage, we estimate the variability of thephysical field as a function of spatial coordinates by approximating itsinformation entropy through the Conditional PixelCNN network. To calculate theentropy, a new ordering of a two-dimensional data array (spiral ordering) isproposed, which makes it possible to obtain the entropy of a physical fieldsimultaneously for several spatial scales. In the second stage, the entropy ofthe physical field is used to initialize the distribution of optimal sensorlocations. This distribution is further optimized with the Concrete Autoencoderarchitecture with the straight-through gradient estimator and adversarial lossto simultaneously minimize the number of sensors and maximize reconstructionaccuracy. Our method scales linearly with data size, unlike commonly usedPrincipal Component Analysis. We demonstrate our method on the two examples:(a) temperature and (b) salinity fields around the Barents Sea and the Svalbardgroup of islands. For these examples, we compute the reconstruction error ofour method and a few baselines. We test our approach against two baselines (1)PCA with QR factorization and (2) climatology. We find out that the obtainedoptimal sensor locations have clear physical interpretation and correspond tothe boundaries between sea currents.

Information Entropy Initialized Concrete Autoencoder for Optimal Sensor Placement and Reconstruction of Geophysical Fields