Detecting and quantifying causality is a focal topic in the fields of science, engineering, and interdisciplinary studies. However, causal studies on non-intervention systems attract much attention but remain extremely challenging. To address this challenge, we propose a framework named Interventional Dynamical Causality (IntDC) for such non-intervention systems, along with its computational criterion, Interventional Embedding Entropy (IEE), to quantify causality. The IEE criterion theoretically and numerically enables the deciphering of IntDC solely from observational (non-interventional) time-series data, without requiring any knowledge of dynamical models or real interventions in the considered system. Demonstrations of performance showed the accuracy and robustness of IEE on benchmark simulated systems as well as real-world systems, including the neural connectomes of C. elegans, COVID-19 transmission networks in Japan, and regulatory networks surrounding key circadian genes.

翻译：检测与量化因果性是科学、工程及交叉学科领域的一个核心议题。然而，针对非干预系统的因果研究虽备受关注，却仍极具挑战性。为应对这一挑战，我们提出了一个名为干预性动态因果性（IntDC）的框架，适用于此类非干预系统，并配套其计算准则——干预嵌入熵（IEE），以量化因果性。IEE准则在理论与数值上均能仅从观测性（非干预性）时间序列数据中破译IntDC，无需任何关于系统动力学模型或实际干预的先验知识。性能验证表明，IEE在基准模拟系统及实际系统中均展现出准确性与鲁棒性，这些系统包括秀丽隐杆线虫的神经连接组、日本COVID-19传播网络以及关键昼夜节律基因周围的调控网络。