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Imagine I want to consider the temperature for a process given several input varibales. The temperature can be anywhere between 400 and 500 K. Consider I have experimental data to train the network and then I want to predict the temperature for a test point. Consider the data as non linear.

As I understand the theory of NN activation function are needed to bound the value between 0 and 1. How could I proceed in my example? Should I just scale my data between 0 and 1? Are there good and bad methods to scale (of course there will be?). Or should I modify the activation function?

However, what if one of the training point's is at 600 K. If I bound the values it would be impossible for the NN to reach this value. I hope someone can give me clarity on this issues.

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As I understand the theory of NN activation function are needed to bound the value between 0 and 1.

No. There are various activation functions, only some of them are bounded (e.g. tanh, sigmoid). One of the most popular activation functions is ReLU which has unbounded positive end. Bounded activation functions are useful for classification and recurrent neural networks, neither of which is your case.

As you are performing regression, just leave the outputs as they are. A neural network with linear output unit should handle it well.

What you might need to scale are the inputs. Neural networks often exhibit better behavior when the inputs are scaled to zero mean and unit variance.

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