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Over the past few years, wireless sensor networks received tremendous attention for monitoring physical phenomena, such as the temperature field in a given region. Applying conventional kernel regression methods for functional learning such as support vector machines is inappropriate for sensor networks, since the order of the resulting model and its computational complexity scales badly with the number of available sensors, which tends to be large. In order to circumvent this drawback, we propose in this paper a reduced-order model approach. To this end, we take advantage of recent developments in sparse representation literature, and show the natural link between reducing the model order and the topology of the deployed sensors. To learn this model, we derive a gradient descent scheme and show its efficiency for wireless sensor networks. We illustrate the proposed approach through simulations involving the estimation of a spatial temperature distribution.