Inferring a network's evolutionary history from a single final snapshot with limited temporal annotations is fundamental yet challenging. Existing approaches predominantly rely on topology alone, which often provides insufficient and noisy cues. This paper leverages network steady-state dynamics -- converged node states under a given dynamical process -- as an additional and widely accessible observation for network evolution history inference. We propose CS$^2$, which explicitly models structure-state coupling to capture how topology modulates steady states and how the two signals jointly improve edge discrimination for formation-order recovery. Experiments on six real temporal networks, evaluated under multiple dynamical processes, show that CS$^2$ consistently outperforms strong baselines, improving pairwise edge precedence accuracy by 4.0% on average and global ordering consistency (Spearman-$ρ$) by 7.7% on average. CS$^2$ also more faithfully recovers macroscopic evolution trajectories such as clustering formation, degree heterogeneity, and hub growth. Moreover, a steady-state-only variant remains competitive when reliable topology is limited, highlighting steady states as an independent signal for evolution inference.

翻译：从仅有的最终快照及有限的时间标注推断网络的演化历史，是一项基础且具有挑战性的任务。现有方法主要依赖拓扑结构本身，其提供的线索往往不足且包含噪声。本文利用网络稳态动力学——即在给定动力学过程下收敛的节点状态——作为推断网络演化历史的另一种广泛可获取的观测信息。我们提出了CS$^2$模型，它显式地对结构-状态耦合进行建模，以捕捉拓扑如何调节稳态，以及这两种信号如何共同改善边形成顺序恢复中的边判别能力。在六个真实时序网络上的实验，通过多种动力学过程进行评估，结果表明CS$^2$始终优于强基线方法，平均将成对边优先顺序准确率提高了4.0%，并将全局排序一致性（Spearman-$ρ$）平均提高了7.7%。CS$^2$还能更准确地恢复宏观演化轨迹，例如聚类形成、度异质性以及枢纽节点增长。此外，当可靠的拓扑信息有限时，一个仅使用稳态的变体模型仍具有竞争力，这凸显了稳态作为演化推断的独立信号的价值。