This work is motivated by the increasing recognition of the neural networks as an emerging modeling technique in microwave area. Appropriate training algorithms are very important in developing neural network models for microwave applications. They decide the amount of training data required, the accuracy that could possibly be achieved, and more importantly the developmental cost of neural models. In this thesis a comprehensive set of training methods suitable for microwave applications has been developed through optimization approaches. These training methods, including quasi Newton method, Huber quasi Newton method, Simplex method, Simulated Annealing algorithm and Genetic algorithm are developed for different training tasks or problems. Accordingly the advantages of the methods upon applications are demonstrated through microwave examples with various neural network structures such as standard feedforward networks, the structures with prior knowledge and wavelet networks.;To especially address the problem of inevitable gross errors in microwave training data, a robust and efficient training algorithm, namely Huber quasi Newton method (HQN) is proposed in this thesis. This algorithm is formulated by combining the Huber concept with the quasi Newton method. Huber concept has been verified to be robust against gross errors and quasi Newton method is considered as the most effective nonlinear optimization method for general problems. The robustness and efficiency of the proposed training algorithm are confirmed by examples in two types of training applications. The first application shows its robustness against gross errors in the training data. The second application uses HQN to learn the smooth behavior of the training data so as to isolate the sharp variation by subtracting the trained model from the training data.
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