Example script showing how to use stateful RNNs to model long sequences efficiently.

library(keras)

# since we are using stateful rnn tsteps can be set to 1
tsteps <- 1
batch_size <- 25
epochs <- 25
# number of elements ahead that are used to make the prediction
lahead <- 1

# Generates an absolute cosine time series with the amplitude exponentially decreasing
# Arguments:
#   amp: amplitude of the cosine function
#   period: period of the cosine function
#   x0: initial x of the time series
#   xn: final x of the time series
#   step: step of the time series discretization
#   k: exponential rate
gen_cosine_amp <- function(amp = 100, period = 1000, x0 = 0, xn = 50000, step = 1, k = 0.0001) {
  n <- (xn-x0) * step
  cos <- array(data = numeric(n), dim = c(n, 1, 1))
  for (i in 1:length(cos)) {
    idx <- x0 + i * step
    cos[[i, 1, 1]] <- amp * cos(2 * pi * idx / period)
    cos[[i, 1, 1]] <- cos[[i, 1, 1]] * exp(-k * idx)
  }
  cos
}

cat('Generating Data...\n')
cos <- gen_cosine_amp()
cat('Input shape:', dim(cos), '\n')

expected_output <- array(data = numeric(length(cos)), dim = c(length(cos), 1))
for (i in 1:(length(cos) - lahead)) {
  expected_output[[i, 1]] <- mean(cos[(i + 1):(i + lahead)])
}

cat('Output shape:', dim(expected_output), '\n')

cat('Creating model:\n')
model <- keras_model_sequential()
model %>%
  layer_lstm(units = 50, input_shape = c(tsteps, 1), batch_size = batch_size,
             return_sequences = TRUE, stateful = TRUE) %>%
  layer_lstm(units = 50, return_sequences = FALSE, stateful = TRUE) %>%
  layer_dense(units = 1)
model %>% compile(loss = 'mse', optimizer = 'rmsprop')

cat('Training\n')
for (i in 1:epochs) {
  model %>% fit(cos, expected_output, batch_size = batch_size,
                epochs = 1, verbose = 1, shuffle = FALSE)

  model %>% reset_states()
}

cat('Predicting\n')
predicted_output <- model %>% predict(cos, batch_size = batch_size)

cat('Plotting Results\n')
op <- par(mfrow=c(2,1))
plot(expected_output, xlab = '')
title("Expected")
plot(predicted_output, xlab = '')
title("Predicted")
par(op)