Should I destandardize the errors from training the neural network?

Question

So, I am learning a bit about Neural Networks. I have built a code in PyTorch for regression, and I have standardized both the features and the target variables following this answer. My question is that should I destandardize the loss value before plotting the elbow curve to observe the train and validation errors across the epochs. I destandardize the predictions on the test dataset to make some plots. But is that necessary for the elbow curve as well? Adding code to make my question a bit more understandable, I guess??

...
x_train = StandardScale(x_train, x_scaler) # Just indicating that scaling is done here
y_train = StandardScale(y_train, y_scaler)
... #Similarly for validation and test datasets ...
dl = DataLoader(params) #for all train, test, val
model = net(params)
optimizer = SGD(model.params(), other-params)
for epoch in range(0, num_epochs):
for i, (x_train, y_train) in enumerate(dl): # This loop is run for both train and val at each epoch.
    optimizer.zero_grad()
    output = model(x_train)
    loss = criterion(output, y_train)
    loss.backward()
    optimizer.step()

    running_loss += loss.item()
...
...
...
epoch_loss = running_loss / len(dl)

history[phase].append(epoch_loss) #history is a dictionary containing training and validation phase losses


fig = plt.figure() #Plotting the elbow plot
plt.plot(history["train"])
plt.plot(history["val"])
y_pred = model(x_test)
y_pred = StandardScaler.inverse_transform(y_pred) # This step is not done for the elbow plot and that is my question.
fig1 = plt.figure() # Plotting the performance on test data
plt.plot(y_pred)
plt.plot(y_test)