Table 1 RNN-GPOD approach to predict the complete field of surface displacements

Offline stage

   1. Generate a numerical model representing the tunnelling process within a selected section of the project from time step 1 to n

   2. Define investigated input parameters and the corresponding range of values

   3. Run numerical simulations with different input parameters

   4. Store the numerical results of displacements of the complete surface area of the analysis section

   5. Provide data of selected monitoring points for the training of a RNN

   6. Provide data of the complete displacements field for training of the POD-RBF

Online stage

   1. Input: an arbitrary set of input parameters

   2. Approximate the complete displacement field from time step 1 to n (by POD-RBF)

   3. Predict the displacements of selected monitoring points for the next time step n+1 (by RNN)

   4. Predict the displacements field for the next time step n+1 (by GPOD)

   5. Update the complete displacements field from time step 1 to n+1

   6. Repeat steps 3–5