Trouble with Neuralnet package in R

Question

I'm trying to compute a neural network with the package neuralnet, to solve a regression problem. I'm trying to approximate the function: f(x1,x2) = sqrt(x1) + sin(x2) + x1*x2.

here is my code:

library(neuralnet)
library(scatterplot3d)
X1 <- as.data.frame(runif(1000, min = 0 , max = 100))
X2 <- as.data.frame(runif(1000, min = 0 , max = 100))
input <- cbind(X1,X2)
sortie <- sqrt(X1) + sin(X2) + X1*X2
donnee <- cbind(sortie,input)
colnames(donnee) <- c("sortie","entree1","entree2")

f <- as.formula(sortie ~ entree1 + entree2)
net.f <- neuralnet(f , donnee, hidden = c(10,10,10) ,linear.output = FALSE)

here is the code to look at the scatterplot of the outputs of the neural networks:

  abscisse1 <- 0:100
  abscisse2 <- 0:100
  net.abscisseformule <- compute(net.f , cbind(abscisse1,abscisse2))
  neuralsortie <-  c(net.abscisseformule$net.result)
  scatterplot3d(abscisse1,abscisse2,neuralsortie)

I'm pretty sure that the result is wrong because the scatterplot doesn't looks like the scatterplot of the function f. I thonk that the problem comes from the line

f <-as.formula(sortie ~ entree1 + entree2)

here is the code to look at the scatterplot of the function

x <- seq(0, 100, 1)
y <- seq(0, 100, 1)
z <- sqrt(x) + sin(y) +x*y
scatterplot3d(x,y,z)

this is the graph of f https://i.stack.imgur.com/HkpbG.png

this is the graph of the outputs of the neuralnet https://i.stack.imgur.com/N38dd.png

Can somebody give me a piece of advice ? Many Thanks !

Answer 1

I find the answer to my question. According to the book The Elements of Statistical Learning (by Friedman,Tibshirani and Hastie), when solving a regression problem it is required to use the identity function in the last layer of the neural network. Which mean that the output is a linear combination of the previous layer. In order to do so with R, it is required to set "linear.output" to TRUE and not FALSE.