Networks of interdependent industrial assets (clients) are tightly coupled through physical processes and control inputs, raising a key question: how would the output of one client change if another client were operated differently? This is difficult to answer because client-specific data are high-dimensional and private, making centralization of raw data infeasible. Each client also maintains proprietary local models that cannot be modified. We propose a federated framework for causal representation learning in state-space systems that captures interdependencies among clients under these constraints. Each client maps high-dimensional observations into low-dimensional latent states that disentangle intrinsic dynamics from control-driven influences. A central server estimates the global state-transition and control structure. This enables decentralized counterfactual reasoning where clients predict how outputs would change under alternative control inputs at others while only exchanging compact latent states. We prove convergence to a centralized oracle and provide privacy guarantees. Our experiments demonstrate scalability, and accurate cross-client counterfactual inference on synthetic and real-world industrial control system datasets.

翻译：相互依赖的工业资产（客户端）网络通过物理过程和控制输入紧密耦合，这引发了一个关键问题：如果另一个客户端的运行方式发生改变，某一客户端的输出将如何变化？由于客户端特定数据具有高维性和隐私性，原始数据的集中化处理并不可行，因此该问题难以回答。每个客户端还维护着专有的本地模型，这些模型不可修改。我们提出了一种用于状态空间系统中因果表征学习的联邦框架，该框架能在上述约束条件下捕捉客户端间的相互依赖关系。每个客户端将高维观测映射到低维潜在状态，从而将内在动力学与控制驱动的影响解耦。中央服务器估计全局状态转移和控制结构。这使得客户端能够进行去中心化反事实推理：在仅交换紧凑潜在状态的前提下，预测当其他客户端采用替代控制输入时自身输出将如何变化。我们证明了该方法能收敛至集中式预言机，并提供了隐私保障。实验结果表明，该方法在合成及真实工业控制系统数据集上具有可扩展性，并能实现精确的跨客户端反事实推理。