Definition of Term: RegularityΒΆ

The output of a simulator is regarded as a function of its inputs. One consideration in building an emulator for the simulator is whether the output is expected to be a continuous function of its inputs, and if so whether it is differentiable. Within the MUCM toolkit, we refer to the continuity and differentiability properties of a simulator as regularity.

The minimal level of regularity would be a simulator whose output is everywhere a continuous function of the inputs, but is not always differentiable. A function which is differentiable everywhere has greater degree of regularity the more times it is differentiable. The most regular of functions are those that are differentiable infinitely many times.