On the Uniqueness of the Discrete Calderón Problem on Multidimensional Lattices

In this work, we investigate the discrete Calderón problem on (hyper)cubic grid graphs in dimension three or higher. The discrete Calderón problem is concerned with determining whether the discrete Dirichlet-to-Neumann matrix, which links boundary potentials to boundary current responses, can uniquely determine the conductivity values on the graph edges. We provide an affirmative answer to the question, thereby extending the classical uniqueness result of Curtis and Morrow for two-dimensional square lattices. The proof employs a slicing technique that decomposes the problem into lower-dimensional components. Additionally, we support the theoretical finding with numerical experiments that illustrate the effectiveness of the approach.