Artificial Neural Networks (ANNs) have been considered an interesting alternative methodology to overcome the drawbacks of mesh-based numerical schemes. Recently, it has been demonstrated that PDEs can be solved by considering a specific ANN called Extreme Learning Machine (ELM). An ELM is a feed-forward neural network with a single hidden layer that randomly assigns the input layer weights and analytically determines the output weights. We point out that ELMs are variants of the random projection networks. Thanks to this architecture, the weights of the hidden layer need not be learned. This makes ELMs faster than typical deep neural networks, where optimization methods may lead to prohibitively slow learning speeds. Overall, randomized Neural Networks boost the learning task with benefits on the numerical scheme in terms of efficiency, while maintaining high accuracy. In this talk we discuss the application of ELMs to PDEs.