Recurrences reveal shared causal drivers of complex time series

Unmeasured causal forces influence diverse experimental time series, such as the transcription factors that regulate genes, or the descending neurons that steer motor circuits. Combining the theory of skew-product dynamical systems with topological data analysis, we show that simultaneous recurrence events across multiple time series reveal the structure of their shared unobserved driving signal. We introduce a physics-based unsupervised learning algorithm that reconstructs causal drivers by iteratively building a recurrence graph with glass-like structure. As the amount of data increases, a percolation transition on this graph leads to weak ergodicity breaking for random walks -- revealing the shared driver's dynamics, even from strongly-corrupted measurements. We relate reconstruction accuracy to the rate of information transfer from a chaotic driver to the response systems, and we find that effective reconstruction proceeds through gradual approximation of the driver's dynamical attractor. Through extensive benchmarks against classical signal processing and machine learning techniques, we demonstrate our method's ability to extract causal drivers from diverse experimental datasets spanning ecology, genomics, fluid dynamics, and physiology.