  We propose a novel learning framework based on neural mean-field dynamics for
inference and estimation problems of diffusion on networks. Our new framework
is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the
node infection probabilities, which renders a delay differential equation with
memory integral approximated by learnable time convolution operators, resulting
in a highly structured and interpretable RNN. Directly using cascade data, our
framework can jointly learn the structure of the diffusion network and the
evolution of infection probabilities, which are cornerstone to important
downstream applications such as influence maximization. Connections between
parameter learning and optimal control are also established. Empirical study
shows that our approach is versatile and robust to variations of the underlying
diffusion network models, and significantly outperform existing approaches in
accuracy and efficiency on both synthetic and real-world data.
