Detecting dynamical causality via intervened reservoir computing

An abundance of complex dynamical phenomena exists in nature and human society, requiring sophisticated analytical tools to understand and explain. Causal analysis through observational time series data is essential in comprehending complex systems when controlled experiments are not feasible or ethical. Although data-based causal discovery methods have been widely used, there is still a lack of direct ways more aligned with the intuitive definition of causality, i.e., whether interventions on one element lead to changes in the subsequent development of others. To solve this problem, we propose the method of intervened reservoir computing (IRC) based on constructing a neural network replica of the original system and applying interventions to it. This approach enables controlled trials, thus observing the intervened evolution, in the digital twins of the underlying systems. Simulated and real-world data are used to test our approach and demonstrate its accuracy in inferring causal networks. Given the importance of causality in understanding complex dynamics, we anticipate that IRC could serve as a powerful tool for various disciplines to decipher the intrinsic mechanisms of natural systems from observational data. Understanding complex systems requires causal analysis via observational time series, yet there is still a lack of direct ways aligned with the intuitive definition of causality. Here, the authors use reservoir computing to replicate the underlying system and apply interventions to it, enabling controlled trials and accurate causal discovery.