Depict noise-driven nonlinear dynamic networks from output data by using high-order correlations

TL;DR

This paper introduces a novel method using high-order correlations to reconstruct nonlinear dynamic network structures from output data, effectively handling noise and nonlinearities simultaneously.

Contribution

It develops a comprehensive theoretical framework combining high-order correlations and two-time correlations for network inference under noise and nonlinear dynamics.

Findings

The method accurately depicts network structures from simulated data.

Theoretical predictions are validated through numerical simulations.

The approach effectively separates noise effects from nonlinear dynamics.

Abstract

Many practical systems can be described by dynamic networks, for which modern technique can measure their output signals, and accumulate extremely rich data. Nevertheless, the network structures producing these data are often deeply hidden in these data. Depicting network structures by analysing the available data, i.e., the inverse problems turns to be of great significant. On one hand, dynamics are often driven by various unknown facts, called noises. On the other hand, network structures of practical systems are commonly nonlinear, and different nonlinearities can provide rich dynamic features and meaningful functions of realistic networks. So far, no method, both theoretically or numerically, has been found to systematically treat the both difficulties together. Here we propose to use high-order correlation computations (HOCC) to treat nonlinear dynamics; use two-time correlations to treat noise effects; and use suitable basis and correlator vectors to unifiedly depict all dynamic nonlinearities and topological interaction links and noise statistical structures. All the above theoretical frameworks are constructed in a closed form and numerical simulations fully verify the validity of theoretical predictions.