Causal inference is fundamental across scientific disciplines, yet existing methods struggle to capture instantaneous, time-evolving causal relationships in complex, high-dimensional systems. In this paper, assimilative causal inference (ACI) is developed, which is a methodological framework that leverages Bayesian data assimilation to trace causes backward from observed effects. ACI solves the inverse problem rather than quantifying forward influence. It uniquely identifies dynamic causal interactions without requiring observations of candidate causes, accommodates short datasets, and, in principle, can be implemented in high-dimensional settings by employing efficient data assimilation algorithms. Crucially, it provides online tracking of causal roles that may reverse intermittently and facilitates a mathematically rigorous criterion for the causal influence range, revealing how far effects propagate. The effectiveness of ACI is demonstrated by complex dynamical systems showcasing intermittency and extreme events. ACI opens valuable pathways for studying complex systems, where transient causal structures are critical.

翻译：因果推断是科学各领域的基础，然而现有方法难以捕捉复杂高维系统中瞬时、时变的因果关系。本文提出了同化因果推断（ACI），这是一个利用贝叶斯数据同化从观测效应反向追踪原因的方法论框架。ACI解决的是逆问题而非量化前向影响。该方法无需候选原因的观测数据即可独特识别动态因果交互，适应短数据集，且原则上可通过采用高效数据同化算法实现高维场景应用。至关重要的是，它提供了对可能间歇反转的因果角色的在线追踪，并为因果影响范围建立了数学严谨的判据，从而揭示效应传播的深度。通过展示间歇性和极端事件的复杂动力系统，验证了ACI的有效性。ACI为研究瞬态因果结构至关重要的复杂系统开辟了重要途径。