Since actually testing nuclear weapons is banned, the only way to verify (ha! verify with simulation) that the current nuclear stockpile is reliable is with simulation. In brief, the idea is to model degradation of current warheads and how that effects their performance/reliability.
For example, the National Ignition Facility (the warp core in Into Darkness) was created partly too provide a source of fusion that could be used to verify the computer models used to simulate nuclear weapon stability. Ie, write a general enough model to see what happens in the fusion bit of a nuke, then apply the model to something like what the NIF does, and then actually test it in the NIF. If the NIF experimental outcomes are in agreement with the model predictions, then we now have higher confidence that the model predictions with regards to the actual nukes are useful.
