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.

翻译：从经验结构和时空观测数据中学习网络动力学，对于揭示广泛领域中复杂网络的交互机制至关重要。然而，现有方法大多仅旨在学习由特定常微分方程实例生成的网络动态行为，导致其难以泛化到新场景，且通常需要密集观测数据。尤其是网络涌现动力学的观测数据往往难以获取，这给模型学习带来了困难。因此，如何利用稀疏、非均匀采样、局部且有噪声的观测数据学习精准的网络动力学仍是一项基本挑战。我们提出面向网络动力学的神经ODE过程（NDP4ND），这是一类由随机数据自适应网络动力学控制的新型随机过程，旨在克服上述挑战并基于稀缺观测数据学习连续网络动力学。在生态种群演化、趋光运动、脑活动、流行病传播及真实世界经验系统等多种网络动力学上开展的密集实验表明，所提方法具有卓越的数据适应性和计算效率，能够适应未见过的网络涌现动力学，实现精准插值与外推，同时将所需观测数据比例降至约6%，并将新动力学的学习速度提升三个数量级。