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：现代工业系统网络日益受到分布式传感器的监控，每个系统包含多个生成高维时序数据的子系统。这些子系统通常相互依赖，因此理解一个子系统的时序模式如何与其他子系统相关联至关重要。这在原始测量数据无法共享且客户端观测具有异构性的去中心化环境中具有挑战性。在实际部署中，每个子系统（客户端）运行固定的专有模型且无法修改或重新训练，这限制了现有方法的适用性。非线性动态特性进一步增加了跨客户端时序依赖关系的解释难度，因为这些依赖关系嵌入在非线性状态转移函数中。本文提出一种在此类约束下学习跨客户端时序依赖关系的联邦框架。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到低维潜在状态。中央服务器通过图注意力网络，基于通信的潜在状态学习图结构神经状态转移模型。为实现可解释性，我们将服务器端学习到的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序依赖关系提供了可解释性表征。我们建立了该框架向集中式基准收敛的理论保证，并通过合成实验验证了其在收敛性、可解释性、可扩展性和隐私保护方面的性能。额外的真实世界实验表明，其性能与去中心化基线方法相当。