A simple neural network in R to predict the square root of numbers.

neuralnet-sqrt.R

library(caret)

# Generate 50 random numbers uniformly distributed between 0 and 100.
training <- data.frame(x = runif(50, min=0, max=100))
training$y <- sqrt(training$x)

# Generate some squared numbers.
cv <- data.frame(x = (1:10)^2)
cv$y <- sqrt(cv$x)

fit <- train(y ~ ., data = training, method = 'neuralnet', tuneGrid = expand.grid(layer1 = c(6), layer2 = 0, layer3 = 0))

results <- predict(fit, newdata = cv)
conf <- table(results, cv$y)

cbind(cv, predict = round(predict(fit, newdata = cv)))

output.txt

With Rounding
---
     x  y predict
1    1  1       2
2    4  2       2
3    9  3       3
4   16  4       4
5   25  5       5
6   36  6       6
7   49  7       7
8   64  8       8
9   81  9       9
10 100 10      10

Raw
---
     x  y     predict
1    1  1 1.556684143
2    4  2 2.114010068
3    9  3 2.975641028
4   16  4 3.987989475
5   25  5 5.004697727
6   36  6 5.998886923
7   49  7 6.997019411
8   64  8 8.000357771
9   81  9 9.003102803
10 100 10 9.992746337