  Spatio-temporal forecasting is of great importance in a wide range of
dynamical systems applications from atmospheric science, to recent COVID-19
spread modeling. These applications rely on accurate predictions of
spatio-temporal structured data reflecting real-world phenomena. A stunning
characteristic is that the dynamical system is not only driven by some physics
laws but also impacted by the localized factor in spatial and temporal regions.
One of the major challenges is to infer the underlying causes, which generate
the perceived data stream and propagate the involved causal dynamics through
the distributed observing units. Another challenge is that the success of
machine learning based predictive models requires massive annotated data for
model training. However, the acquisition of high-quality annotated data is
objectively manual and tedious as it needs a considerable amount of human
intervention, making it infeasible in fields that require high levels of
expertise. To tackle these challenges, we advocate a spatio-temporal
physics-coupled neural networks (ST-PCNN) model to learn the underlying physics
of the dynamical system and further couple the learned physics to assist the
learning of the recurring dynamics. To deal with data-acquisition constraints,
an active learning mechanism with Kriging for actively acquiring the most
informative data is proposed for ST-PCNN training in a partially observable
environment. Our experiments on both synthetic and real-world datasets exhibit
that the proposed ST-PCNN with active learning converges to near optimal
accuracy with substantially fewer instances.
