Deep neural network (DNN)-based methods are suitable for the rapid inversion of borehole resistivity measurements. They approximate the forward and the inverse problem offline during the training phase, and they only require a fraction of a second for the online evaluation (aka prediction). Herein, we have adopted a DNN-based iterative algorithm to design a borehole instrument such that the inverse solution is unique for a given earth parameterization. We select a large set of electromagnetic measurement systems routinely used in logging operations, and our DNN algorithm selects a subset of measurements that are suitable for inversion purposes. Numerical results with synthetic data confirm that this approach can provide valuable insight when designing borehole-logging instruments.