Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients
Francesco Calabrò,
Gianluca Fabiani,
Constantinos Siettos
Abstract:We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a single hidden layer with sigmoidal functions and fixed, random, internal weights and biases can be used to compute accurately a collocation solution. The choice to fix internal weights and bias leads to the so-called Extreme Learning Machine network. We discuss how to determine t… Show more
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