We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that the linearization of this non-linear inverse problem admits a unique solution. Our method is inspired by a method to study local uniqueness of inverse problems with internal functionals in the continuum, where the inverse problem is reformulated as a redundant system of differential equations. We use our method to derive local uniqueness conditions for other discrete inverse problems with internal functionals including a discrete analogue of the inverse Schr\"odinger problem and problems where the resistors are replaced by impedances and dissipated power at the zero and a positive frequency are available. Moreover, we show that the dissipated power measurements can be obtained from measurements of thermal noise induced currents.

翻译：我们研究从不同负载下电阻器耗散功率的测量值中确定电阻网络内电阻器参数的问题。我们给出了保证局部唯一性的充分条件，即确保该非线性逆问题的线性化存在唯一解的条件。我们的方法受到连续介质内函数逆问题局部唯一性研究方法的启发，该方法将逆问题重构为冗余微分方程组。我们运用该方法推导了其他离散内函数逆问题的局部唯一性条件，包括逆薛定谔问题的离散模拟，以及用阻抗替代电阻且能获取零频率与正频率下耗散功率的问题。此外，我们证明了耗散功率测量值可通过热噪声感应电流的测量获得。