Deep Koopman operator framework for causal discovery in nonlinear dynamical systems

Juan Nathaniel, Carla Roesch, Jatan Buch, Derek DeSantis, Adam Rupe, Kara D Lamb, Pierre Gentine

Keywords: Koopman, dynamical systems, causal discovery, climate science, deep learning

TL;DR: We introduce Kausal, a deep Koopman operator-theoretic formalism, to disentangle cause-effect mechanisms for improved scientific understanding of physical world models.

Abstract: We use a deep **K**oopman operator-theoretic formalism to develop a novel c**ausal** 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.

Submission Number: 14