Resumen
This paper presents a new method for finding the optimal positions for sensors used to reconstruct geophysical fields from sparse measurements. The method is composed of two stages. In the first stage, we estimate the spatial variability of the physical field by approximating its information entropy using the Conditional Pixel CNN network. In the second stage, the entropy is used to initialize the distribution of optimal sensor locations, which is then optimized using the Concrete Autoencoder architecture with the straight-through gradient estimator for the binary mask and with adversarial loss. This allows us to simultaneously minimize the number of sensors and maximize reconstruction accuracy. We apply our method to the global ocean under-surface temperature field and demonstrate its effectiveness on fields with up to a million grid cells. Additionally, we find that the information entropy field has a clear physical interpretation related to the mixing between cold and warm currents.