Reconstructing dissipative dynamical systems from spatially and temporally sparse sensors

The reconstruction of fields from sensor data is a common task in scientific applications. In many cases, the observation is under resolved, and memory must be incorporated to uniquely recover the underlying system. For dissipative systems, dynamical systems theory provides guidance in formulating these data-driven reconstructions, which has been the focus of many optimization and machine learning approaches. Most models are restricted to data sampled at fixed positions and regular time intervals. We introduce a model which overcomes these limitations using attention mechanisms with spatial and temporal encodings. Our model is based on the Senseiver, which reconstructs fields from instantaneous sparse sensor measurements. Informed by time delay embedding theorems, we formulate an attention-based model that learns from and generalizes to sensor data at varying spatial position and sampling rates. We evaluate the model on systems exhibiting a limit cycle and spatiotemporal chaos.