Solving a directed percolation inverse problem

TL;DR

This paper introduces an inverse problem for directed percolation in diode networks, proposing an iterative method to reconstruct network configurations from partial current flow data, outperforming exhaustive approaches especially in complex cases.

Contribution

The paper develops a divide-and-concur iterative projection method for solving the directed percolation inverse problem, demonstrating its effectiveness over exhaustive methods.

Findings

The method outperforms exhaustive search on nontrivial instances.

Reconstruction difficulty peaks when some data are hidden.

Networks with sensitive currents are hardest to reconstruct.

Abstract

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.