Given a complex system with a given interface to the rest of the world, what does it mean for a the system to behave close to a simpler specification describing the behavior at the interface? We give several definitions for useful notions of distances between a complex system and a specification by combining a behavioral and probabilistic perspective. These distances can be used to tune a complex system to a specification. We show that our approach can successfully tune non-linear networked systems to behave like much smaller networks, allowing us to aggregate large sub-networks into one or two effective nodes. Finally, we discuss similarities and differences between our approach and H∞ model reduction.

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Given two dynamical systems, we quantify how similar they are with respect to their interaction with the outside world. We focus on the case where simpler systems act as a specification for a more complex one. Combining a behavioral and probabilistic perspective we define several useful notions of the distance of a system to a specification.

We show that these distances can be used to tune a complex system. We demonstrate that our approach can successfully make non-linear networked systems behave like much smaller networks, allowing us to aggregate large sub-networks into one or two effective nodes. Finally, we discuss similarities and differences between our approach and H∞ model reduction.