Accelerated reference frames (ARFs) reveal networks from time series data

Abstract

Inferring direct interactions in complex networked systems from time series data constitutes a challenging open problem of current research. Major obstacles include the often limited number of time points accessible, unknown or inaccurate dynamical systems models in many practical applications, the impossibility to infer topological information from invariant collective dynamics such as synchronized states, and the required computational effort. Here, we propose and analyze a mathematical scheme that transforms observed transient dynamics towards invariant states in to accelerated reference frames to reveal network interactions. The transformation yields simple linear constraints relating a number of short observed time series (of only a few data points) of the dynamics to estimates the absence, presence and strength of direct physical interactions in a computationally efficient way. As we illustrate numerically, the scheme applies across transient dynamics towards periodic and chaotic, phase-locked and other synchronized states. Reconstruction robustly reveals the entire connectivity of network dynamical systems with increased reconstruction quality for large and for sparse networks.

Inferring connectivity of an oscillatory network via the phase dynamics reconstruction

“…We illustrate the performance of the approach for the Winfree-type model with random coupling functions (containing p = 3 harmonics) and a fully connected random network of 16 oscillators in Figure 3. Similar approaches to reconstruction of large oscillatory networks have been discussed by Casadiego and Timme (2018), Panaggio et al (2019), Tokuda et al (2019), Novaes et al (2021), andRings et al (2022). We mention that there is still a problem of discriminating small couplings from nonexisting ones.…”

Inferring interactions of time-delayed dynamic networks by random state variable resetting

“…In recent years, researchers have explored approaches to inferring the interactions by solving ordinary differential equations (ODEs). Some detection methods can be used to reconstruct a linear dynamic network, [16][17][18][19] while expanding basis [20][21][22][23][24] and expanding variable [25,26] methods are proposed to detect a general nonlinear dynamic network. These methods not only reveal connections, but also provide information on local dynamics and coupling functions.…”