Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell’s, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.

The role of human resources has become a key factor for the success of an organization. Based on a research collaboration with an aeronautical company, the paper proposes a comparison of two different approaches for the reconstruction of a collaborative social network in the business realm: the use of traditional Social Network Analysis and novel statistical inference models. Both approaches were evaluated against data provided by the company, in order to scout the key people in the network and the knowledge-transfer processes. As a main outcome of this paper, it was found how the network reconstruction using statistical models has an increased robustness, as well as sensitivity, allowing to discover hidden correlations among the users.