Neural network alternative to the Nicholson-Ross-Weir algorithm for complex permittivity extraction of non-magnetic materials at microwave frequencies

At microwave frequencies, the electromagnetic (EM) characterization of materials is not possible through direct measurements. In this case, the Nicholson-Ross-Weir (NRW) algorithm is the standard phenomenological analytical approach for the inverse problem. The algorithm finds the equivalent complex permittivity and permeability, starting from scattering parameters at two terminals of a waveguide structure containing the material. To be successful, NRW needs a material sample thin enough, and careful operations with complex valued logarithm. When successful, extracted parameters have round-off errors, but when not, the results are wrong. Thus, the inverse problem of the EM material characterization at microwave frequencies is an interesting benchmark for optimization algorithms and machine learning alternatives. A neural network alternative is investigated in this paper for the case of non-magnetic materials, operating at a fixed frequency. This is a necessary first step before approaching neural network (NN) models valid for whole frequency ranges and magneto-dielectric materials. A feed forward NN with one hidden layer was used, its hyperparameters being tuned by employing a multi-objective optimization procedure. Numerical results show that a NN carefully chosen can provide accurate results for a relatively large domain of complex permittivity components, being successful in areas where NRW fails. The implementation, carried out in python with Optuna module, is available for free download.