Deep Koopman operator framework for causal discovery in nonlinear dynamical systems

We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. In Kausal, we propose to leverage Koopman operators for causal analysis where optimal observables are inferred using deep learning. Our numerical experiments with toy models and real-world phenomena such as El Niño-Southern Oscillation demonstrate Kausal's superior ability in discovering and characterizing causal signals compared to existing approaches. Code is publicly available at https://github.com/juannat7/kausal.