Using Neural Networks to compute one log curve from others is a method that gained great popularity in the 1990s; however, it is not well suited to geophysical applications, such as:
Repairing / Replacing Sonic Logs
Repairing / Replacing Density Logs
Replacing / Repairing Shear Logs
Neural networks use local training to estimate local values. This will tend to be valid when applied to a single zone across a single field, but will tend to break down when applied to the entire section across a wide area.
Because the form of each petrophysical relationship is already known from rock physics experiments, multivariate nonlinear regression is better than neural nets for these applications. But the computational phase of the log editing process is the easy part: what separates success from failure is the recognition of good data and exclusion of bad data from training sets. What matters is the judgment of the analyst. Obviously the analyst's judgement will be best developed if the mathematics are consistent from project to project over time.