Model reduction of large networked systems using the Manifold Boundary Approximation Method

Complex systems are often described by a network.
Models of these systems are often constructed from physical first principles by accounting for the interaction network among the components.
For large systems, model complexity grows faster than the richness of the available data, leading to many more tunable parameters than can be reliably estimated from measurements.
The resulting models are often sloppy and amenable to effective descriptions in which mechanistic details are intentionally ignored in favor of the relevant collective degrees of freedom governing system behavior.
We consider the case of a small network model from electric power systems and show that sloppiness is manifest in both dynamic and network parameters.
Using techniques of information geometry, we derive reduced models of the network that act as effective theories in cases where only partial system measurements are available using the Manifold Boundary Approximation Method (MBAM).
Leveraging insights from this model, we apply a linearized version of MBAM to a much larger system.
We demonstrate that this method can identify the effective network of interactions, and discuss implications for modeling of other networked systems.