Physics-inspired machine learning detects 'unknown unknowns' in networks: discovering network boundaries from observable dynamics

Dynamics on networks is often only partially observable in experiment, with many nodes being inaccessible or indeed the existence and properties of a larger unobserved network being unknown. This limits our ability to reconstruct the topology of the network and the strength of the interactions among even the observed nodes. Here, we show how machine learning inspired by physics can be utilized on noisy time series of such partially observed networks to determine which nodes of the observed part of a network form its boundary, i.e. have significant interactions with the unobserved part. This opens a route to reliable network reconstruction. We develop the method for arbitrary network dynamics and topologies and demonstrate it on a broad range of dynamics including non-linear coupled oscillators and chaotic attractors. Beyond these we focus in particular on biochemical reaction networks, where we apply the approach to the dynamics of the epidermal growth factor receptor (EGFR) network and show that it works even for substantial noise levels.