Networks that arise in fields such as biology or energy present features that challenge established modelling setups since the target function may naturally live on edges, node and/or edge (covariate) data may be available, the (edge-)function may be evolving through time (e.g., dropping in/out), and the data may depart from the stationarity assumption. This project will tackle general network data setups, to include time, node or edge missingness and/or nonstationarity, and it will give rise to new realistic models and associated estimation theory across a variety of tasks from regression to forecasting, resulting in theory-based context-informed analysis. The consequent multiscale network representation will be conducive to additionally solving associated tasks such as clustering, e.g., highlighting genes associated to plant disease resistance. Although the project stems from applications in biology and energy, the methodology we will develop will also be highly relevant in other fields such as the neurosciences, e.g. for the analysis of brain functional connectivity.