4.3 Neural Network Training

The most important and time-consuming step in model development is neural network training. A neural network learns the microwave behavior throughthis process. The neural network would be taught with measured/simulated samples from the training set. Conventional training of neural networks is an optimization process in the weight space using optimization-based training algorithms. The most popular training algorithm in neural network literature is back propagation (BP). However, for most of the microwave modeling problems, second-order training algorithms such as conjugate-gradient, and Quasi-Newton are more efficient. From the optimization point of view, the training process adjusts w such that the error between neural model predictions and desired outputs is minimized, that is, min E( w), where E( w) = E _{T r}( w).

The objective function E( w) (see (4.4) and (4.5)) is a nonlinear function of the adjustable weight parameters w. Due to the complexity of E( w), iterative algorithms are used to explore the weight space. In iterative methods, we start with an initial guess of w and then iteratively update w as

(4.30)