R Notebook

Simulating Neural network to build a model for basic Sinosudal function

Loading Neural Network library

library(neuralnet)

Generating test data & Assigining names to test data

train<-as.data.frame(cbind((sample(1:600, 300, replace=FALSE))))
train<-cbind(train,pi/train$V1)
colnames(train) <- c("Input","Output")
train

Simulating neural network with a single hidden layer and ten neurons.

n.net <- neuralnet( formula = Output~Input, data = train, hidden=c(10), threshold=0.0001,lifesign = "full",lifesign.step = 1000)

hidden: 10    thresh: 0.0001    rep: 1/1    steps:    1000  min thresh: 0.003012459516
                                                      2000  min thresh: 0.001127379782
                                                      3000  min thresh: 0.0004023896783
                                                      4000  min thresh: 0.0004023896783
                                                      5000  min thresh: 0.0004023896783
                                                      6000  min thresh: 0.0004023896783
                                                      7000  min thresh: 0.0004023896783
                                                      8000  min thresh: 0.000186737906
                                                      8608  error: 0.00008  time: 2.55 secs

#print(n.net)

Let’ see what our network looks like

plot(n.net)

Generating Test data to validate out network

test<-as.data.frame(setdiff(1:60,train$Input))#as.data.frame(c(31:60))
names(test)<-"Input"
test

Now running test data on the generated model

result<-compute(n.net,test)
result$net.result

               [,1]
 [1,] 0.79256867601
 [2,] 0.52393927586
 [3,] 0.26404453350
 [4,] 0.22776063038
 [5,] 0.21272152542
 [6,] 0.18710782998
 [7,] 0.17614411018
 [8,] 0.15727134043
 [9,] 0.14186415219
[10,] 0.13526470155
[11,] 0.12392301739
[12,] 0.11905084781
[13,] 0.11060730070
[14,] 0.10355302790
[15,] 0.09753993527
[16,] 0.09483592317
[17,] 0.08544573495
[18,] 0.08136613685
[19,] 0.07578268698
[20,] 0.07072133073
[21,] 0.06760261519
[22,] 0.06328296308
[23,] 0.06193547841
[24,] 0.06063303070
[25,] 0.05816034718
[26,] 0.05372056030

Combining results

test<-cbind(test,result$net.result,(pi/test$Input))
colnames(test)<-c("Input","Neural Output","Computed Output")

test

Lets round the numbers and have a look at them.

round(test,2)

SO we have successfully simulated a neural network for a formula f(x) = PI/x. Our accuracy is 99.9919%