Computation of the dispersion relations of photonic crystals by using multilayer perceptron (MLP) and extreme learning machine artificial neural networks. This technique has been used to bi- and tridimensional optimized structures presenting distinct dispersion relations and photonic bandgaps. The optical properties of a set of photonic crystals with similar geometries and different dimensions can be analyzed by an electromagnetic solver in order to provide the input data for artificial neural network training and testing. This technique has demonstrated to be simple- and fast-training artificial neural network models and be capable of providing accurate dispersion relations curves in a very short time. This subject is part of a PhD dissertation supervised by Dr. Hugo E. H. Figueroa and has been published at the Journal of Lightwave Technology, Vol. 36, no. 18, September 15, 2018