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,tan(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(10,5), threshold=0.001,lifesign = "full",lifesign.step = 1000)

hidden: 10, 5    thresh: 0.001    rep: 1/1    steps:    1000    min thresh: 0.005405457351
                                                        2000    min thresh: 0.001846320338
                                                        3000    min thresh: 0.001846320338
                                                        4000    min thresh: 0.001412758764
                                                        5000    min thresh: 0.001106107449
                                                        5527    error: 0.00011  time: 2.57 secs

#print(n.net)

n1.net <- neuralnet( formula = Output~Input, data = train, hidden=c(10,5), threshold=0.0001,lifesign = "full",lifesign.step = 1000
                     ,startweights=n.net$weights)

hidden: 10, 5    thresh: 0.0001    rep: 1/1    steps:    1000   min thresh: 0.0008768371493
                                                         2000   min thresh: 0.0006944589611
                                                         3000   min thresh: 0.0003810472056
                                                         4000   min thresh: 0.0002721542456
                                                         5000   min thresh: 0.0001539876516
                                                         6000   min thresh: 0.0001539876516
                                                         7000   min thresh: 0.0001539876516
                                                         8000   min thresh: 0.0001539876516
                                                         9000   min thresh: 0.0001539876516
                                                        10000   min thresh: 0.0001539876516
                                                        11000   min thresh: 0.0001539876516
                                                        12000   min thresh: 0.0001539876516
                                                        13000   min thresh: 0.0001539876516
                                                        14000   min thresh: 0.0001539876516
                                                        15000   min thresh: 0.0001539876516
                                                        16000   min thresh: 0.0001539876516
                                                        17000   min thresh: 0.0001264070201
                                                        17875   error: 0.00001  time: 8.62 secs

#print(n.net)

Let’ see what our network looks like

plot(n1.net)

Generating Test data to validate out network

#test<-as.data.frame(setdiff(1:600,train$Input))#as.data.frame(c(31:60))
test<-as.data.frame(c(1:100))#as.data.frame(c(31:60))
names(test)<-"Input"
head(test)

Now running test data on the generated model

result<-compute(n1.net,test)
head(result$net.result)

                 [,1]
[1,] 0.00001084349734
[2,] 2.21136635687555
[3,] 1.73199727896773
[4,] 1.00015120849479
[5,] 0.70690106834471
[6,] 0.57688969627637

Combining results

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

test

Lets round the numbers and have a look at them.

head(round(test,2))

SO we have successfully simulated a neural network for a formula f(x) = tan(PI/x). Our accuracy is 99.99994% Althought the accuravy is high, we see an outlier at Input = 2. To avoid this neural network must be trained for all extreme scenarios. Except the outlier the model accurately gives results.