When we have a numerical model that represents a real physical system, and that exhibits chaos (e.g. fluid dynamics models, climate models), how can we know that the model is performing as it should? We cannot compare two sets of model output directly, because even small changes in initial conditions will dramatically change the outputs of individual simulations. We cannot compare the model output directly to observations, either because we can never know with enough detail the initial conditions of the observations, and numerical approximation would anyway cause minor differences that would propagate through the system.
This question is partly inspired by David Ketcheson's question on unit testing scientific code: I'm particularly interested in how regression tests for such models could be implemented. If a minor initial conditions change can lead to major output changes (which may well still be adequate representations of reality), then how can we separate those changes from changes caused by modifying parameters, or implementing new numerical routines?