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.