If you have the permeability given NMR measurements and want to model permeability as function of NMR and depth, you can easily build your NN model by assign NMR and Depth as independent variables and permeability as response variable to start the training procedure.

you can implement that in Matlab or R.

Please find the given attachment or go through publication in the following link.

https://www.onepetro.org/conference-paper/SPE-126042-MS