  We propose a novel learning framework using neural mean-field (NMF) dynamics
for inference and estimation problems on heterogeneous diffusion networks. Our
new framework leverages the Mori-Zwanzig formalism to obtain an exact evolution
equation of the individual node infection probabilities, which renders a delay
differential equation with memory integral approximated by learnable time
convolution operators. Directly using information diffusion cascade data, our
framework can simultaneously learn the structure of the diffusion network and
the evolution of node infection probabilities. Connections between parameter
learning and optimal control are also established, leading to a rigorous and
implementable algorithm for training NMF. Moreover, we show that the projected
gradient descent method can be employed to solve the challenging influence
maximization problem, where the gradient is computed extremely fast by
integrating NMF forward in time just once in each iteration. Extensive
empirical studies show 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.
