Scaling laws for infrastructure-native computation

Determine whether operator representation, controllability, multiplexing capacity, and task performance in infrastructure-native computing follow predictable scaling laws as electric-network size increases from the IEEE 14-bus benchmark to larger systems such as the IEEE 33-bus and IEEE 118-bus networks, and establish whether the observed 13.2-fold operator-representation advantage grows monotonically with system size.

Background

The paper compares a 933-parameter surrogate representation of the IEEE 14-bus operator with a 12,340-parameter fully connected replacement. It notes that sparse grid topologies may require approximately O(N) independent physical parameters, whereas fully connected digital representations may require O(N²) parameters for comparable dimensionality.

However, the single 14-bus experiment does not determine how representation size, controllability, multiplexing, or classification performance change in larger networks. The authors identify larger IEEE benchmark systems as tractable test cases for resolving whether the apparent structural advantage has predictable and scalable behavior.

References

Finally, the scaling of computational capacity with network size remains an open empirical question. For sparse grid topologies in which the number of branches scales approximately with the number of buses, the number of independent physical parameters determining the network operator can scale approximately as \mathrm{O}(\mathrm{N}), whereas a fully connected digital representation of comparable dimensionality contains \mathrm{O}(\mathrm{N}2) free parameters . The present 14-bus comparison is consistent with this structural difference, but it does not establish that the measured 13.2-fold advantage will grow monotonically with system size. Larger benchmark networks, such as the IEEE 33-bus and IEEE 118-bus systems , provide tractable test cases for determining whether operator representation, controllability, multiplexing capacity, and task performance follow predictable scaling relationships.

— Infrastructure-Native Computing with Electric Power Grids  (2610.08390 - Song et al., 6 Oct 2026) in Discussions, final paragraph