Nice Way to Track Sensitivity of Model to Parametric/Functional Perturbations When Model Can Be Simulated but Not Solved Exactly

I was wondering if you new any nice sensitivity test measures for models, where the model is implicitly defined via a system of nonlinear PDEs/difference equations that would be computationally feasible to implement. I was thinking of using something like sampling from the parameter space and simulating the solutions at different parameters via a Quasi- Monte Carlo method and then using kriging or something similar to fit a functional form approximation that has a built-in measure of uncertainty. Not sure if there are better ways, however, and what I would really like to do is get a nonparametric sensitivity analysis to a change in a functional form assumption, which makes it a lot harder.