Related papers: Deep Koopman operator framework for causal discovery in nonlinear dynamical systems

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems

URL: http://arxiv.org/abs/2505.14828v1
Date: Tue, 20 May 2025 18:43:48 GMT
Title: Deep Koopman operator framework for causal discovery in nonlinear dynamical systems
Authors: Juan Nathaniel, Carla Roesch, Jatan Buch, Derek DeSantis, Adam Rupe, Kara Lamb, Pierre Gentine,
Abstract summary: We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal.<n>kausal aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling.<n>Our numerical experiments demonstrate Kausal's superior ability in discovering and characterizing causal signals.
Score: 0.08813517558695427
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. 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. This presents a challenge in studying many real-world systems, such as the Earth's climate. Meanwhile, Koopman operator methods have emerged as a promising tool for approximating nonlinear dynamics in a linear space of observables. In Kausal, we propose to leverage this powerful idea for causal analysis where optimal observables are inferred using deep learning. Causal estimates are then evaluated in a reproducing kernel Hilbert space, and defined as the distance between the marginal dynamics of the effect and the joint dynamics of the cause-effect observables. Our numerical experiments demonstrate Kausal's superior ability in discovering and characterizing causal signals compared to existing approaches of prescribed observables. Lastly, we extend our analysis to observations of El Ni\~no-Southern Oscillation highlighting our algorithm's applicability to real-world phenomena. Our code is available at https://github.com/juannat7/kausal.

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