In this section, we will use the same simulated dataset that we created in the previous section of this recipe, Sequential API. Here, we will create a multi-output functional model:

1. Let's start by importing the required library and create an input layer:

library(keras)

# input layer
inputs <- layer_input(shape = c(784))

2. Next, we need to define two outputs:

predictions1 <- inputs %>%
 layer_dense(units = 8)%>%
 layer_activation('relu') %>%
 layer_dense(units = 1,name = "pred_1")

predictions2 <- inputs %>%
 layer_dense(units = 16)%>%
 layer_activation('tanh') %>%
 layer_dense(units = 1,name = "pred_2")

3. Now, we need to define a functional Keras model:

model_functional = keras_model(inputs = inputs,outputs = c(predictions1,predictions2))

Let's look at the summary of the model:

summary(model_functional)

The following screenshot shows the model's summary:

4. Now, we compile our model:

model_functional %>% compile(
 loss = "mse",
 optimizer = optimizer_rmsprop(),
 metrics = list("mean_absolute_error")
)

5. Next, we need to train the model and visualize the model's parameters:

history_functional <- model_functional %>% fit(
 x_data,
 list(y_data,y_data),
 epochs = 30,
 batch_size = 128,
 validation_split = 0.2
 )

Now, let's plot the model loss for the training and validation data of prediction 1 and prediction 2:

# Plot the model loss of the prediction 1 training data
plot(history_functional$metrics$pred_1_loss, main="Model Loss", xlab = "epoch", ylab="loss", col="blue", type="l")

# Plot the model loss of the prediction 1 validation data
lines(history_functional$metrics$val_pred_1_loss, col="green")

# Plot the model loss of the prediction 2 training data
lines(history_functional$metrics$pred_2_loss, col="red")

# Plot the model loss of the prediction 2 validation data
lines(history_functional$metrics$val_pred_2_loss, col="black")

# Add legend
legend("topright", c("training loss prediction 1","validation loss prediction 1","training loss prediction 2","validation loss prediction 2"), col=c("blue", "green","red","black"), lty=c(1,1))

The following plot shows the training and validation loss for both prediction 1 and prediction 2:

Now, let's plot the mean absolute error for the training and validation data of prediction 1 and prediction 2:

# Plot the model mean absolute error of the prediction 1 training data
plot(history_functional$metrics$pred_1_mean_absolute_error, main="Mean Absolute Error", xlab = "epoch", ylab="error", col="blue", type="l")

# Plot the model mean squared error of the prediction 1 validation data
lines(history_functional$metrics$val_pred_1_mean_absolute_error, col="green")

# Plot the model mean squared error of the prediction 2 training data
lines(history_functional$metrics$pred_2_mean_absolute_error, col="red")

# Plot the model mean squared error of the prediction 2 validation data
lines(history_functional$metrics$val_pred_2_mean_absolute_error, col="black")

# Add legend
legend("topright", c("training mean absolute error prediction 1","validation mean absolute error prediction 1","training mean absolute error prediction 2","validation mean absolute error prediction 2"), col=c("blue", "green","red","black"), lty=c(1,1))

The following plot shows the mean absolute errors for prediction 1 and prediction 2: