Modeling Randomly Observed Spatiotemporal Dynamical Systems

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.