Tharusha Bandara | Search arXiv

arXiv2026

Transferable reconstruction of nonlinear network dynamics from sentinel nodes

Reconstructing the state of a large networked system from measurements at only a few nodes is a challenge for monitoring, prediction, and intervention. Here we ask whether such reconstruction is possible and whether it can transfer across different nonlinear dynamics. We study this question across various networks and across $16$ nonlinear dynamics on networks from different domains. For each network, we observe only a vanishingly small fraction of sentinel nodes and train either a neural network or linear decoder. We find that accurate reconstruction is often possible, and that transferability is structured rather than universal. Eleven dynamics with adjacency-matrix-type coupling form a robust transferable class. By contrast, five diffusively coupled dynamics form isolated transfer components. Non-random sentinel selection is consistently important, and linear decoders often approach neural-network performance. These results show that sparse node observations can encode enough information to reconstruct full network equilibria across broad families of nonlinear dynamics, while also revealing sharp limits to universal transfer.

physics.soc-ph↗

arXiv2026

Baseline-referenced spatial early warning signals for tipping points on heterogeneous networks

Anticipating tipping points in complex systems is difficult because many early warning signals require long time series, which are often unavailable in practice. Spatial early warning signals offer an alternative by using a single snapshot across many interacting elements, or nodes. However, their performance in heterogeneous systems is often inconsistent because raw node states reflect both dynamical changes associated with an approaching transition and static heterogeneity induced by network structure. Here, we propose a baseline-referenced framework for spatial early warning signals. The method compares each node's state with its own baseline far from the tipping point before computing a spatial statistic, thus reducing network-structure-induced variation. We evaluate baseline-referenced variants of five classical spatial early warning signals across diverse tipping scenarios and networks, and find that baseline referencing markedly improves variance-based spatial signals. The best variants increase consistently and progressively toward tipping points across different scenarios, outperform a single-node temporal variance that requires long time series, and retain high performance even when up to 80% of nodes are omitted from observation. These results provide a practical route for using spatial early warning signals in heterogeneous networked systems when dense temporal monitoring or complete network-wide observation is infeasible, as is often the case in real applications.

physics.soc-ph↗