  Large quantifies of online user activity data, such as weekly web search
volumes, which co-evolve with the mutual influence of several queries and
locations, serve as an important social sensor. It is an important task to
accurately forecast the future activity by discovering latent interactions from
such data, i.e., the ecosystems between each query and the flow of influences
between each area. However, this is a difficult problem in terms of data
quantity and complex patterns covering the dynamics. To tackle the problem, we
propose FluxCube, which is an effective mining method that forecasts large
collections of co-evolving online user activity and provides good
interpretability. Our model is the expansion of a combination of two
mathematical models: a reaction-diffusion system provides a framework for
modeling the flow of influences between local area groups and an ecological
system models the latent interactions between each query. Also, by leveraging
the concept of physics-informed neural networks, FluxCube achieves high
interpretability obtained from the parameters and high forecasting performance,
together. Extensive experiments on real datasets showed that FluxCube
outperforms comparable models in terms of the forecasting accuracy, and each
component in FluxCube contributes to the enhanced performance. We then show
some case studies that FluxCube can extract useful latent interactions between
queries and area groups.
