基于相对平衡时通用动力学的网络耦合单快照推断
Single-Snapshot Inference of Network Couplings from Universal Dynamics at Relative Equilibrium
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中文总结 AI 辅助
研究如何从单个快照推断网络耦合强度，利用系统相对平衡时节点共享共同速度的特性，将反问题转化为齐次线性系统，通过观测局部邻域及其耦合机制确定系数，在三个动力系统上验证，可实现隐藏耦合强度的单快照推断。
中文摘要 AI 辅助
许多现实世界系统可建模为复杂网络，其集体行为由节点间隐藏相互作用支配。现有推断这些相互作用的方法通常需要可控扰动、时间分辨观测或多个独立快照，而实际中往往无法获取。本文表明，当系统在相对平衡附近被观测时，可从节点状态的单个快照推断基于类的耦合强度。在此状态下，所有节点共享共同速度，可被吸收到有效类偏差中，将反问题转化为齐次线性系统。该线性系统的系数完全由观测到的局部邻域及其耦合机制确定，可应用于任意已知耦合函数。我们在三个不同的线性和非线性动力系统上验证了该方法，恢复了基于类的相对耦合，在特殊情况下还恢复了绝对耦合。这些结果表明空间异质性可替代时间采样，实现网络动力系统中隐藏耦合强度的单快照推断。
英文摘要
Many real-world systems can be modelled as complex networks whose collective behaviour is governed by hidden interactions between nodes. Existing methods for inferring these interactions typically require controlled perturbations, time-resolved observations or multiple independent snapshots, all of which are often unavailable in practice. Here we show that class-based coupling strengths can be inferred from a single snapshot of node states when the system is observed close to a relative equilibrium. In this regime, all nodes share a common velocity, which can be absorbed into an effective class bias, transforming the inverse problem into a homogeneous linear system. The coefficients of this linear system are determined entirely by the observed local neighbourhoods and their coupling mechanism, enabling the application to arbitrary known coupling functions. We validate the approach on three different linear and nonlinear dynamical systems, recovering relative class-based couplings and, in special cases, absolute couplings. These results show that spatial heterogeneity can substitute for temporal sampling, enabling single-snapshot inference of hidden coupling strengths in networked dynamical systems.
