Optimal noise-canceling networks
Provides theoretical principles for designing noise-filtering networks, relevant to engineers and biologists dealing with noisy inputs.
The paper analytically and numerically explores the design of noise-canceling networks using phase oscillator arrays, finding that optimal architectures become sparser and more hierarchical as input correlations increase, offering principles for robust power grids and sensor networks.
Natural and artificial networks, from the cerebral cortex to large-scale power grids, face the challenge of converting noisy inputs into robust signals. The input fluctuations often exhibit complex yet statistically reproducible correlations that reflect underlying internal or environmental processes such as synaptic noise or atmospheric turbulence. This raises the practically and biophysically relevant of question whether and how noise-filtering can be hard-wired directly into a network's architecture. By considering generic phase oscillator arrays under cost constraints, we explore here analytically and numerically the design, efficiency and topology of noise-canceling networks. Specifically, we find that when the input fluctuations become more correlated in space or time, optimal network architectures become sparser and more hierarchically organized, resembling the vasculature in plants or animals. More broadly, our results provide concrete guiding principles for designing more robust and efficient power grids and sensor networks.