Reconstructing dynamical networks via feature ranking

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the structure of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as “features” and use two independent feature ranking approaches—Random Forest and RReliefF—to rank the importance of each node for predicting the value of each other node, which yields the reconstructed adjacency matrix. We show that our method is fairly robust to coupling strength, system size, trajectory length, and noise. We also find that the reconstruction quality strongly depends on the dynamical regime. Recent technological developments make empirical data on complex systems from different scientific areas increasingly available. Yet, precise equations governing them remain elusive. As a consequence, there is a need for methods for inferring the structure of these complex systems from the available data. A good example are methods for network reconstruction from time-resolved observations of their node dynamics. Crucial here are assumptions one is ready to make about the underlying system when developing the method. Diverse methods have been proposed based on physical insights about the nature of the system (for example, limit-cycle oscillations). While making the method elegant, these assumptions often (severely) limit the method’s applicability in a realistic setting. Here we seek to design a method with minimal assumptions possible. We resort to machine learning and interpret the available data (time series) as “features.” Relying on two different feature ranking approaches, we rank the importance of each node for predicting the value of any other node. This information, as we show, reconstructs the network’s adjacency matrix. Our method is fairly robust to coupling strength, system size, trajectory length, and noise, thus making it suitable for practical applications in a broad spectrum of complex systems.The study was financially supported by the Slovenian Research Agency through research core funding of programs P1-0383, Complex Networks (Z.L.), P2-0103 (B.Ž.), and P5-0093 (L.T.), as well as projects J5-8236 (Z.L.) and N2-0056, Machine Learning for Systems Sciences (L.T.). M.G.L. and Z.L. acknowledge funding from the EU via H2020 Marie Sklodowska-Curie project COSMOS (Grant No. 642563), and B.Ž. acknowledges funding from the EU via H2020 projects SAAM (Grant No. 769661) and RESILOC (Grant No. 833671)