Multivalued Neural Network Inverse Modeling and Applications to Microwave Filters

This paper presents a new technique for artificial neural network (ANN) inverse modeling and applications to microwave filters. In inverse modeling of a microwave component, the inputs to the model are electrical parameters such as S-parameters, and the outputs of the model are geometrical or physical parameters. Since the analytical formula of the inverse input-output relationship does not exist, the ANN becomes a logical choice, because it can be trained to learn from the data in inverse modeling. The main challenge of inverse modeling is the nonuniqueness problem. This problem in the ANN inverse modeling is that different training samples with the same or very similar input values have quite different (contradictory) output values (multivalued solutions). In this paper, we propose a multivalued neural network inverse modeling technique to associate a single set of electrical parameters with multiple sets of geometrical or physical parameters. One set of geometrical or physical parameters is called one value of our proposed inverse model. Our proposed multivalued neural network is structured to accommodate multiple values for the model output. We also propose a new training error function to focus on matching each training sample using only one value of our proposed inverse model, while other values are free and can be trained to match other contradictory samples. In this way, our proposed multivalued neural network can learn all the training data by automatically redirecting contradictory information into different values of the proposed inverse model. Therefore, our proposed technique can solve the nonuniqueness problem in a simpler and more automated way compared with the existing ANN inverse modeling techniques. This technique is illustrated by inverse modeling and parameter extraction of four microwave filter examples.