[mturmon]

It's also worth saying that there's an emerging discipline devoted to formalizing and developing tools for this kind of problem (complex computer models of real-world systems, say).

One decent place to start is this National Academies report [1] on Verification, Validation, and Uncertainty Quantification.

Verification = did you implement the math correctly in the computer;

Validation = does the implemented mathematical model compare against the real system in controlled experimentss

Uncertainty Quantification = analysis and prediction of the accuracy of the model approximation.

This work was given a big push by the nuclear test ban treaty - you have to really validate the model predictions in this case.

[1] https://www.nap.edu/catalog/13395/assessing-the-reliability-...