#remove comment sign (#) from output
knitr::opts_chunk$set(echo = TRUE, message = FALSE, comment = "")

The necessary package

library(neuralnet)

simulated variables

xol = sample(500)
yat = rnorm(500, mean= 350,sd=0.5)
aef = 2*xol
bwy = xol + yat
cak = yat - xol*0.5

Data table

dta = data.frame(xol,yat,aef,bwy,cak) 
head(dta) # the first 6 rows 
  xol      yat aef      bwy      cak
1  94 349.9780 188 443.9780 302.9780
2  24 349.8200  48 373.8200 337.8200
3 460 350.8300 920 810.8300 120.8300
4 452 350.6014 904 802.6014 124.6014
5 327 350.0243 654 677.0243 186.5243
6 362 350.4095 724 712.4095 169.4095

The neural network model with multiple hidden layers and two output nodes

dtnet = neuralnet(xol + yat ~ aef + bwy + cak, hidden=c(10,5), data = dta, linear.output=T)

The net plot

plot(dtnet, rep="best")

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