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ON NUMERICAL RECOVERY METHODS FOR THE INVERSE PROBLEM

In this paper, we present the approaches we took to recover the conductances of an electrical network, concentrating on the method of nonlinear least squares optimization. The methods include steepest descent with symbolic differentiation and numerical differentiation, Newton’s method, and Levenberg-Marquardt. Using these algorithms, we were able to recover large networks. In order to better reflect real life situations, we decided to add noise to our measurements and include some knowledge of the resistors. This led us to add a regularization term and try a method of rounding between iterations. In the end, without any a priori knowledge, we recovered a 50x50 square lattice network with constant conductance to within 0.01% error.