  Locally interacting dynamical systems, such as epidemic spread, rumor
propagation through crowd, and forest fire, exhibit complex global dynamics
originated from local, relatively simple, and often stochastic interactions
between dynamic elements. Their temporal evolution is often driven by
transitions between a finite number of discrete states. Despite significant
advancements in predictive modeling through deep learning, such interactions
among many elements have rarely explored as a specific domain for predictive
modeling. We present Attentive Recurrent Neural Cellular Automata (AR-NCA), to
effectively discover unknown local state transition rules by associating the
temporal information between neighboring cells in a permutation-invariant
manner. AR-NCA exhibits the superior generalizability across various system
configurations (i.e., spatial distribution of states), data efficiency and
robustness in extremely data-limited scenarios even in the presence of
stochastic interactions, and scalability through spatial dimension-independent
prediction.
