  Spatiotemporal processes are a fundamental tool for modeling dynamics across
various domains, from heat propagation in materials to oceanic and atmospheric
flows. However, currently available neural network-based modeling approaches
fall short when faced with data collected randomly over time and space, as is
often the case with sensor networks in real-world applications like
crowdsourced earthquake detection or pollution monitoring. In response, we
developed a new spatiotemporal method that effectively handles such randomly
sampled data. Our model integrates techniques from amortized variational
inference, neural differential equations, neural point processes, and implicit
neural representations to predict both the dynamics of the system and the
probabilistic locations and timings of future observations. It outperforms
existing methods on challenging spatiotemporal datasets by offering substantial
improvements in predictive accuracy and computational efficiency, making it a
useful tool for modeling and understanding complex dynamical systems observed
under realistic, unconstrained conditions.
