  Learning network dynamics from the empirical structure and spatio-temporal
observation data is crucial to revealing the interaction mechanisms of complex
networks in a wide range of domains. However, most existing methods only aim at
learning network dynamic behaviors generated by a specific ordinary
differential equation instance, resulting in ineffectiveness for new ones, and
generally require dense observations. The observed data, especially from
network emerging dynamics, are usually difficult to obtain, which brings
trouble to model learning. Therefore, how to learn accurate network dynamics
with sparse, irregularly-sampled, partial, and noisy observations remains a
fundamental challenge. We introduce Neural ODE Processes for Network Dynamics
(NDP4ND), a new class of stochastic processes governed by stochastic
data-adaptive network dynamics, to overcome the challenge and learn continuous
network dynamics from scarce observations. Intensive experiments conducted on
various network dynamics in ecological population evolution, phototaxis
movement, brain activity, epidemic spreading, and real-world empirical systems,
demonstrate that the proposed method has excellent data adaptability and
computational efficiency, and can adapt to unseen network emerging dynamics,
producing accurate interpolation and extrapolation with reducing the ratio of
required observation data to only about 6\% and improving the learning speed
for new dynamics by three orders of magnitude.
