Self-averaging enables reconstruction of higher-order chaotic networks

Higher-order interactions create a combinatorial space of candidate dynamical terms, making network reconstruction difficult when node dynamics, coupling functions and interaction topology are unknown. Here we identify a regime in which weakly coupled higher-order chaotic networks admit a higher-order interaction reduction. Weak coupling largely preserves the statistical structure of intrinsic chaotic motion, while dense higher-order neighborhoods provide repeated sampling of weakly correlated multi-node inputs received by hub nodes. Consequently, the aggregate interaction field can be represented by a compact function of the hub state, together with a node-dependent offset and finite-neighborhood fluctuations. We exploit this reduction to learn dynamically relevant coupling forms and reconstruct interactions of different orders by sparse regression. Numerical experiments validate the effectiveness of the framework within an effective region of the tested coupling-parameter space, including representative weak-coupling settings. Reconstruction remains stable at the larger network sizes and higher hub-neighborhood densities examined. Additional tests on networks constructed from empirical topologies show that structural priors reduce data requirements and that the framework remains applicable to heterogeneous chaotic dynamics. These results identify reduction of aggregate higher-order inputs as an interpretable route to dimensional compression and joint dynamical and structural reconstruction.