State estimation of urban air pollution with statistical, physical, and super-learning graph models

Data-driven estimations are becoming increasingly relevant and widespread as the volume and heterogeneity of available data increases. A fundamental challenge is to build numerical methods for which one can estimate how optimally they exploit the given information. The present paper addresses some essential computational aspects connected to this question. More specifically, our goal is to reconstruct a state u of a physical process, for which we have at hand very heterogeneous sources of data coming from direct partial observations of u, from quantities related to u, and from the knowledge that the physics can be modelled by a Partial Differential Equations (PDE).