A statistical physics approach to optimization of network controllability ​

The problem of the controllability of the dynamical state of a network is central in network theory. Using the framework of structural controllability, it is possible to find the minimum number of driver nodes, i.e. the nodes that can bring the network to the desired dynamical state if an external input is applied to them. The minimum number of driver nodes can be found with Belief Propagation (BP) algorithms. In this work, we show a new procedure that optimizes the network controllability via minimal structural perturbation of the network. It is performed with a BP-guided Simulated Annealing procedure: on each trial, we find the minimal number of driver nodes via BP equations, and then we perform a second optimization that selects, through minimization of a cost function, a well-controlled configuration with the minimum number of driver nodes, obtained with the minimum number of added edges. The outcomes are compared with other algorithms in the literature. A possible development of this work via a two levels equations is presented in the concluding part of the thesis.