Rupe, A., DeSantis, D., Bakker, C., Kooloth, P., & Lu, J. (2024). Causal Discovery in Nonlinear Dynamical Systems using Koopman Operators. arXiv preprint arXiv:2410.10103v1.
This paper aims to address the limitations of traditional statistical causal inference methods in analyzing nonlinear dynamical systems by proposing a novel framework based on Koopman operators. The authors seek to provide a rigorous definition of causal mechanisms in dynamical systems and develop a data-driven algorithm for quantifying causal relations.
The authors ground their theory on a definition of causal mechanisms in dynamical systems based on flow maps, which are then translated into the Koopman framework. They prove the equivalence between the flow map definition and the Koopman definition of causal mechanisms. Leveraging the Koopman framework's global linearization property, they develop a data-driven algorithm based on Dynamic Mode Decomposition (DMD) to quantify multivariate causal relations from data.
The proposed Koopman theory of causality offers a powerful new approach for causal discovery in nonlinear dynamical systems. It provides a theoretically sound framework and a practical data-driven algorithm for identifying and quantifying causal relations, even in high-dimensional systems with complex interactions.
This research significantly contributes to the field of causal inference by extending its applicability to nonlinear dynamical systems, which are prevalent in various domains like climate science and fluid dynamics. The proposed framework and algorithm offer valuable tools for understanding complex system behaviors and identifying causal drivers.
The paper primarily focuses on theoretical foundations and initial demonstrations of the Koopman causality framework. Further research is needed to explore its performance on real-world datasets with higher complexity and noise. Additionally, investigating the robustness of the DMD-based algorithm to different data sampling rates and dictionary choices would be beneficial.
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by Adam Rupe, D... at arxiv.org 10-15-2024
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