Solving a directed percolation inverse problem
This addresses a specific inverse problem in network reconstruction for diode systems, with incremental improvements in solving such configurations.
The paper tackles the directed percolation inverse problem in diode networks, aiming to reconstruct diode configurations from observed current percolation data, and demonstrates that their divide-and-concur iterative projection method outperforms exhaustive approaches for nontrivial instances.
We present a directed percolation inverse problem for diode networks: Given information about which pairs of nodes allow current to percolate from one to the other, can one find a configuration of diodes consistent with the observed currents? We implement a divide-and-concur iterative projection method for solving the problem and demonstrate the supremacy of our method over an exhaustive approach for nontrivial instances of the problem. We find that the problem is most difficult when some but not all of the percolation data are hidden, and that the most difficult networks to reconstruct generally are those for which the currents are most sensitive to the addition or removal of a single diode.