Spatio-Temporal Causality for Turbulence via Attention Learning

Causality is fundamental to scientific discovery, yet most existing inference methods are ill-suited to capture the full spatio-temporal complexity of high-dimensional dynamical systems. We present an attention-based causal inference framework grounded in Wiener's definition of causality. Given a source and target field, the method assigns causal scores to the source as functions of space and time, enabling a hierarchical decomposition of global causal influence into localized spatio-temporal contributions. The framework employs a Vision Transformer Autoencoder to compress high-dimensional input fields into latent representations, with causal influence extracted via multi-head self-attention over time-lagged embeddings. We validate the method on controlled spatio-temporal benchmarks with known causal structure and demonstrate its ability to correctly recover ground-truth causal patterns. We further apply the approach to turbulent channel flow to uncover the causal link between streamwise velocity fluctuations and wall shear stress. Our results show that causality is state-dependent and varies with prediction horizon: at short horizons, high-speed streaks exert increasing causal influence with intensity, while at longer horizons, their influence fades and low-speed streaks become dominant.