Loss Functions¶

Choosing a suitable loss function for the task at hand can make a significant difference, primarily depending on the dataset targets. In order to give you a certain freedom in this sense (i.e. when it comes to weighting outliers), Fortnet implements the following functions:

mean squared loss (mse)

root mean square loss (rms)

mean absolute loss (mae)

mean absolute percentage loss (mape)

The loss function used during the training is selected in the Training block of the HSD input. The functions and an associated, exemplary training block, are listed below, assuming a dataset of \(N\) targets \(y_i^\mathrm{ref}\) and network predictions \(y_i^\mathrm{nn}\).

Note

The default loss function is the mean squared error (mse).

Mean Squared Error¶

\[\begin{align*} C = \frac{1}{N}\sum_{i=1}^N \left(y_i^\mathrm{ref} - y_i^\mathrm{nn}\right)^2 \end{align*}\]

Training = LBFGS {
      .
      .
      .
  Loss = 'mse'
}

Root Mean Square Error¶

\[\begin{align*} C = \sqrt{\frac{1}{N}\sum_{i=1}^N \Big(y_i^\mathrm{ref} - y_i^\mathrm{nn}\Big)^2} \end{align*}\]

Training = LBFGS {
      .
      .
      .
  Loss = 'rms'
}

Mean Absolute Error¶

\[\begin{align*} C = \frac{1}{N}\sum_{i=1}^N |y_i^\mathrm{ref} - y_i^\mathrm{nn}| \end{align*}\]

Training = LBFGS {
      .
      .
      .
  Loss = 'mae'
}

Mean Absolute Percentage Error¶

\[\begin{align*} C = \frac{100}{N}\sum_{i=1}^N \frac{|y_i^\mathrm{ref} - y_i^\mathrm{nn}|} {|y_i^\mathrm{ref}|} \end{align*}\]

Training = LBFGS {
      .
      .
      .
  Loss = 'mape'
}