AI 中文总结
该研究提出基线参考空间预警信号框架，通过对比节点状态与自身基线减少网络结构变异，显著提升异质网络临界点预警性能，适用于观测条件有限的实际场景。
AI 中文摘要
预测复杂系统中的临界点十分困难，因为许多早期预警信号需要长时间序列，而实际中往往无法获得。空间预警信号提供了一种替代方案，它利用众多相互作用元素（或节点）的单一快照来实现。然而，它们在异质系统中的表现通常不一致，因为原始节点状态既反映了与逼近转变相关的动力学变化，也反映了网络结构导致的静态异质性。在此，我们提出一种用于空间预警信号的基线参考框架。该方法将每个节点的状态与其远离临界点时的自身基线进行比较，然后计算空间统计量，从而减少网络结构引起的变异。我们在不同的临界点场景和网络上评估了五种经典空间预警信号的基线参考变体，发现基线参考显著提升了基于方差的空间信号的性能。最佳变体在不同场景下会朝着临界点持续且逐步增强，其表现优于需要长时间序列的单节点时间方差，即使在多达80%的节点被排除在观测之外时仍保持高性能。这些结果为在密集时间监测或完整全网络观测不可行的异质网络系统中应用空间预警信号提供了实用途径，而这在实际应用中往往是常见情况。
英文摘要
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.
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