Journey over destination: dynamic sensor placement enhances generalization

Reconstructing complex, high-dimensional global fields from limited data points is a challenge across various scientific and industrial domains. This is particularly important for recovering spatio-temporal fields using sensor data from, for example, laboratory-based scientific experiments, weather forecasting, or drone surveys. Given the prohibitive costs of specialized sensors and the inaccessibility of certain regions of the domain, achieving full field coverage is typically not feasible. Therefore, the development of machine learning algorithms trained to reconstruct fields given a limited dataset is of critical importance. In this study, we introduce a general approach that employs moving sensors to enhance data exploitation during the training of an attention based neural network, thereby improving field reconstruction. The training of sensor locations is accomplished using an end-to-end workflow, ensuring differentiability in the interpolation of field values associated to the sensors, and is simple to implement using differentiable programming. Additionally, we have incorporated a correction mechanism to prevent sensors from entering invalid regions within the domain. We evaluated our method using two distinct datasets; the results show that our approach enhances learning, as evidenced by improved test scores.