Application of Neural Network Method to Restore the Refraction Index of Homogeneous Dielectric Layer
Dmitry N. Tumakov
Diana M. Khairullina
The research studied the problem of a homogeneous layer refraction value recovering by Neural Network Method. The case with the known thickness is studied. We used three neuron activation functions: a linear, a sigmoidal and Gauss function. The network training is conducted by two methods: the method of back propagation and genetic algorithm. The desired value of refraction index is chosen as the average one between the results of independent neural networks trained according to the same initial data. This approach makes sense because the target functions of networks comprise the plurality of local extrema and each new network with a random initial vector of weights provides different but close results. The method of cross validation estimarted the accuracy of refractive index recovery for different activation functions and the methods of network training. The conclusion that the genetic algorithm provides better results than the gradient methods (in particular, the method of error backpropagation). It was shown that the number of neurons increase leads to a natural improvement of recoverable values accuracy for refractive index. The best objective functions are obtained for neural networks with sigmoidal and Gaussian activation function. It is expressed by more sustainable behavior of error at continuous change of other network settings. The plots of error dependence for the recovery of the refractive index on the sample size and the number of neurons are presented which confirm the findings.