Many physical, biological and social challenges are the result of a compromise between competing factors. Mesoscience addresses the problem of predicting the outcome of such competition, and extends over many diverse disciplines; examples abound in the sciences, engineering, medicine, economics, weather forecasting, climate change and the political and social sciences. In the simplest instances, e.g. the determination of the thermodynamic conditions for two phases, such as a gas and a liquid, to coexist in equilibrium, the principles are well known and prediction is straightforward. However, most cases of interest are dynamic, evolving in time, and can involve numerous competing factors.