Revealing physical interaction networks from statistics of collective dynamics

Abstract

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of detail often not available. We exploit changes in invariant measures, in particular distributions of sampled states of the system in response to driving signals, and use compressed sensing to reveal physical interaction networks. Dynamical observations following driving suffice to infer physical connectivity even if they are temporally disordered, are acquired at large sampling intervals, and stem from different experiments. Testing various nonlinear dynamic processes emerging on artificial and real network topologies indicates high reconstruction quality for existence as well as type of interactions. These results advance our ability to reveal physical interaction networks in complex synthetic and natural systems.

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

“…n N 0 i  -. Whereas exactly synchronous or phase-locked dynamics in principle can generally not reveal the complete network topology, inferring from transient dynamics towards synchrony or locking was so far restricted to driving-response settings with known signals [16] or to general model-free approaches using a large repertoire of functions [11,12,14,15]. While the former strategy allows to create linear mappings from recorded dynamics to network topology, the latter allows to infer links from transient dynamics following an unknown driving or perturbation.…”

“…Such approaches require the entire dynamics to admit a sparse representation in the chosen repertoire, which is difficult to satisfy if no prior information is provided. More recent approaches bypass the need for sparsity and reconstruct the full interaction topology by either imposing functional decompositions in grouped variables [15], or by driving the network dynamics with known constant signals [16]. While the former strategy carries along a high computational complexity that may become intractable in large networks, the latter demands an accurate (and often infeasible) control of network dynamics.…”

Physically-interpretable classification of biological network dynamics for complex collective motions

“…dynamical) information for multiple types of collective motions. Previous other approaches have extracted linear dynamics in complex networks [34] and physical interaction networks [35].…”

Reconstructing dynamical networks via feature ranking

“…In this setting, the problem of network reconstruction reduces to estimating the presence/absence of links between the pairs of nodes from time-resolved measurements of their dynamics (time series), which are assumed available. It is within this formulation that we approach the topic in this paper, i.e., we consider the structure of the studied network to be hidden in a "black box", and seek to reconstruct it from time series of node dynamics (i.e., discrete trajectories).Within the realm of physics literature, many methods have been proposed relying on above formulation of the problem, and are usually anchored in empirical physical insights about network collective behavior [46,52,74]. This primarily includes synchronization [3], both theoretically [2,58] and experimentally [6,36], and in the presence of noise [72].…”

“…For example, these methods often require the knowledge of not just the mathematical form of the dynamical model, but also the precise knowledge of the interaction function(s) [39,43]. Similarly, some methods require the possibility to influence the system under study, for example by resetting its dynamics or influencing it in other ways [42,52]. Other methods make assumptions about the dynamical nature of the available trajectories (data), e.g., their linearity.…”