Networks of modern industrial systems are increasingly monitored by distributed sensors, where each system comprises multiple subsystems generating high dimensional time series data. These subsystems are often interdependent, making it important to understand how temporal patterns at one subsystem relate to others. This is challenging in decentralized settings where raw measurements cannot be shared and client observations are heterogeneous. In practical deployments each subsystem (client) operates a fixed proprietary model that cannot be modified or retrained, limiting existing approaches. Nonlinear dynamics further make cross client temporal interdependencies difficult to interpret because they are embedded in nonlinear state transition functions. We present a federated framework for learning temporal interdependencies across clients under these constraints. Each client maps high dimensional local observations to low dimensional latent states using a nonlinear state space model. A central server learns a graph structured neural state transition model over the communicated latent states using a Graph Attention Network. For interpretability we relate the Jacobian of the learned server side transition model to attention coefficients, providing the first interpretable characterization of cross client temporal interdependencies in decentralized nonlinear systems. We establish theoretical convergence guarantees to a centralized oracle and validate the framework through synthetic experiments demonstrating convergence, interpretability, scalability and privacy. Additional real world experiments show performance comparable to decentralized baselines.

翻译：现代工业系统的网络日益由分布式传感器监测，每个系统包含多个生成高维时间序列数据的子系统。这些子系统通常相互依赖，因此理解一个子系统的时间模式与其他子系统的关系至关重要。在无法共享原始测量数据且客户端观测存在异质性的去中心化环境下，这一任务具有挑战性。实际部署中，每个子系统（客户端）运行固定的专有模型，无法修改或重新训练，从而限制了现有方法。非线性动力学进一步使跨客户端时间依赖性的解释变得困难，因为其嵌入在非线性状态转移函数中。我们提出了一种联邦学习框架，用于在上述约束下学习客户端间的时间依赖性。每个客户端使用非线性状态空间模型将高维局部观测映射至低维潜在状态。中央服务器利用图注意力网络对通信的潜在状态进行图结构神经状态转移模型的学习。为实现可解释性，我们将所学习的服务器端转移模型的雅可比矩阵与注意力系数相关联，首次为去中心化非线性系统中的跨客户端时间依赖性提供了可解释的表征。我们建立了理论收敛性保证，证明其收敛至集中式最优解，并通过合成实验验证了收敛性、可解释性、可扩展性和隐私性。额外的真实世界实验表明其性能可与去中心化基线方法相媲美。