Small data analytics, at the opposite extreme of big data analytics, represents a critical limitation in structural health monitoring based on spaceborne remote sensing technology. Besides the engineering challenge, small data is a typical demanding issue in machine learning applications related to the prediction of system evolutions. To address this challenge, this article proposes a parsimonious yet robust predictive model obtained as a combination of a regression artificial neural network and of a Bayesian hyperparameter optimization. The final aim of the offered strategy consists of the prediction of limited/small structural responses extracted from synthetic aperture radar images in remote sensing. Results regarding a long-span steel arch bridge confirm that, although simple, the proposed method can effectively predict the structural response in terms of displacement data with a noteworthy overall performance.