Learning Spatiotemporal Dynamical Systems from Point Process Observations

TL;DR

This paper introduces a novel neural network-based method that effectively learns complex spatiotemporal dynamics from irregularly timed and located point process data, outperforming existing approaches in accuracy and efficiency.

Contribution

The authors develop an integrated model combining neural differential equations, point processes, and variational inference to handle irregular spatiotemporal data for the first time.

Findings

Significant improvement in predictive accuracy over existing methods

Enhanced computational efficiency in modeling complex systems

Effective handling of real-world, unconstrained observation data

Abstract

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when faced with data that is 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 method that can effectively learn spatiotemporal dynamics from such point process observations. Our model integrates techniques from neural differential equations, neural point processes, implicit neural representations and amortized variational inference to model both the dynamics of the system and the probabilistic locations and timings of 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.