Neural networks with multidimensional transfer functions

Abstract

We present a new type of neural network (NN) where the data for the input layer are the value x in R, the vector y in R(m ) associated to an initial value problem (IVP) with y'(x)= f(y(x)) and a steplength h. Then the stages of a Runge-Kutta (RK) method with trainable coefficients are used as hidden layers for the integration of the IVP using f as transfer function. We take as output two estimations y*, y;* of IVP at the point x+h. Training the RK method at some test problems and counting the cost of the method under the coefficients used, we may achieve coefficients that help the method to perform better at a wider class of problems.