  Complex systems are characterized by intricate interactions between entities
that evolve dynamically over time. Accurate inference of these dynamic
relationships is crucial for understanding and predicting system behavior. In
this paper, we propose Regulatory Temporal Interaction Network Inference
(RiTINI) for inferring time-varying interaction graphs in complex systems using
a novel combination of space-and-time graph attentions and graph neural
ordinary differential equations (ODEs). RiTINI leverages time-lapse signals on
a graph prior, as well as perturbations of signals at various nodes in order to
effectively capture the dynamics of the underlying system. This approach is
distinct from traditional causal inference networks, which are limited to
inferring acyclic and static graphs. In contrast, RiTINI can infer cyclic,
directed, and time-varying graphs, providing a more comprehensive and accurate
representation of complex systems. The graph attention mechanism in RiTINI
allows the model to adaptively focus on the most relevant interactions in time
and space, while the graph neural ODEs enable continuous-time modeling of the
system's dynamics. We evaluate RiTINI's performance on various simulated and
real-world datasets, demonstrating its state-of-the-art capability in inferring
interaction graphs compared to previous methods.
