Neural Networks for RF and Microwave Design

4.10: Feedforward Neural Network Training: Examples

4.10 Feedforward Neural Network Training: Examples

In this section, three conductor microstripline and physics-based MESFET modeling examples are used to compare the performance of various training algorithms for feedforward neural networks namely, the adaptive back propagation, conjugate-gradient, Quasi-Newton, and Levenberg-Marquardt algorithms [2].

For the microstripline example, there are five input neurons corresponding to conductor width ( w), spacing between conductors ( s 1, s 2), substrate height ( h), and relative permittivity ( ? r), as shown in Figure 4.29. There are six output neurons corresponding to the self-inductance of each conductor ( L 11, L 22, L 33), and the mutual inductance between any two conductors ( L 12, L 23, L 13). A total of 600 training samples and 640 test samples were generated using LINPAR [54]. A three-layer MLP structure with 28 hidden neurons was used, and the training results are shown in Table 4.4. The CPU time was given for a 200 MHz Pentium.


Figure 4.29: A three-conductor microstripline.
Table 4.4: Comparison of Various Training Algorithms for Microstripline Example (from [2], Wang, F., et al., "Neural Network Structures and Training Algorithms for RF and Microwave Applications," Int. J. RF and Microwave CAE, pp. 216 240, 1999, John Wiley and Sons. Reprinted with permission from John Wiley and Sons, Inc.).

Training Algorithm

No. of Epochs

Training Error (%)

Avg. Test Error (%)

CPU (in Sec)

Adaptive back propagation

10,755

0.224

0.252

13,724

Conjugate-gradient

2,169

0.415

0.473

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