Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved hidden drivers on the observed dynamics. This paper presents a unified method capable of identifying fundamental causal relationships between pairs of systems, whether deterministic or stochastic. Notably, the method also uncovers hidden common causes beyond the observed variables. By analyzing the degrees of freedom in the system, our approach provides a more comprehensive understanding of both causal influence and hidden confounders. This unified framework is validated through theoretical models and simulations, demonstrating its robustness and potential for broader application.

翻译：时间演化系统通常通过动态方程进行建模。精确建模的一个关键挑战在于理解子系统间的因果关系，以及识别未观测到的隐藏驱动因素对观测动态的存在和影响。本文提出了一种统一方法，能够识别成对系统之间的基本因果关系，无论系统是确定性的还是随机的。值得注意的是，该方法还能揭示超出观测变量的隐藏共同原因。通过分析系统的自由度，我们的方法提供了对因果影响和隐藏混杂因素更全面的理解。这一统一框架通过理论模型和仿真实验得到验证，证明了其鲁棒性和更广泛应用的潜力。