Lie-Algebraic Neural Koopman Dynamics
Jiwoong Kim, Jongwon Lee, Jungwoo Park, Sungwoo Park
Abstract
We present a Lie-algebraic approach to model Koopman dynamics that integrates algebraic structure with computational scalability. The proposed formulation constrains the neural generators to evolve within prescribed Lie subalgebras and constructs finite-time flows through a neural Magnus expansion construction, thereby maintaining consistency with the associated Lie-group composition over each time segment. To address the computational burden inherent in sequential propagation, we exploit the associativity of Lie-group compositions and construct segmentwise propagators via a prefix-scan algorithm, which reduces the depth of temporal composition from linear to logarithmic. Consequently, the framework enables accurate long-horizon prediction while improving computational efficiency, and provides a principled foundation for scalable Koopman operator learning for nonlinear systems.
BibTeX
@inproceedings{
lee2026liealgebraic,
title={Lie-Algebraic Acceleration of Neural Koopman Dynamics},
author={Jongwon Lee and Jiwoong Kim and Jungwoo Park and Sungwoo Park},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=EVlt6J7PGR}
}