Conformal Online Learning of Deep Koopman Linear Embeddings
Ben Gao, Jordan Patracone, Stephane Chretien, Olivier Alata
Abstract
We introduce Conformal Online Learning of Koopman embeddings (COLoKe), a novel framework for adaptively updating Koopman-invariant representations of nonlinear dynamical systems from streaming data. Our modeling approach combines deep feature learning with multistep prediction consistency in the lifted space, where the dynamics evolve linearly. To prevent overfitting, COLoKe employs a conformal-style mechanism that shifts the focus from evaluating the conformity of new states to assessing the consistency of the current Koopman model. Updates are triggered only when the current model’s prediction error exceeds a dynamically calibrated threshold, allowing selective refinement of the Koopman operator and embedding. Empirical results on benchmark dynamical systems demonstrate the effectiveness of COLoKe in maintaining long-term predictive accuracy while significantly reducing unnecessary updates and avoiding overfitting.
BibTeX
@inproceedings{
gao2025conformal,
title={Conformal Online Learning of Deep Koopman Linear Embeddings},
author={Ben Gao and Jordan Patracone and Stephane Chretien and Olivier Alata},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=O8Ifwhylnr}
}