Every physics analysis that uses a NN goes through the process of validating their network and almost always derives systematic uncertainties to cover issues, e.g. data vs. MC.
This approach can vary and can be specific to the use case. However, general approaches and best practices can be outlined.
One reasonable method is to simply vary the input variable by their uncertainties and take the NN output variation as the systematic. However, this may not always be sufficient.
This topic has been discussed in past ML forums: https://indico.cern.ch/event/1154231/
PHYSTAT: https://indico.cern.ch/event/1172085/