Scalable Infinitesimal Generator–Based Koopman Learning for Long-Horizon Prediction

Minseok Jeong, SooJean Han, Hyo-Sang Shin
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1966-1980, 2026.

Abstract

Koopman operator theory offers a linear representation of nonlinear dynamics and has strong potential for long-horizon prediction. However, most existing methods rely on one-step snapshot fitting and suffer from error accumulation over long rollouts. Prior work has attempted to address this by extending training horizons or using physics-informed, generator-based formulations. Still, these approaches remain limited, partly because they rely on MLP-based observables, whose spectral bias favors low-frequency components. In this paper, we introduce a Random Fourier Feature–lifted physics-informed Koopman network (RFF-PIKN) that directly minimizes the generator loss. We first show that snapshot-based local transition fitting has inherent limitations in long-horizon stability relative to generator-based learning. We then prove that RFF-PIKN converges stably to a local minimizer of the true population risk under the generator loss. Finally, empirical comparisons demonstrate that RFF-PIKN outperforms MLP- and polynomial-based observables in long-horizon prediction while substantially reducing computation, and further matches key behaviors of oracle kernel-based methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-jeong26a, title = {Scalable Infinitesimal Generator–Based Koopman Learning for Long-Horizon Prediction}, author = {Jeong, Minseok and Han, SooJean and Shin, Hyo-Sang}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1966--1980}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/jeong26a/jeong26a.pdf}, url = {https://proceedings.mlr.press/v331/jeong26a.html}, abstract = {Koopman operator theory offers a linear representation of nonlinear dynamics and has strong potential for long-horizon prediction. However, most existing methods rely on one-step snapshot fitting and suffer from error accumulation over long rollouts. Prior work has attempted to address this by extending training horizons or using physics-informed, generator-based formulations. Still, these approaches remain limited, partly because they rely on MLP-based observables, whose spectral bias favors low-frequency components. In this paper, we introduce a Random Fourier Feature–lifted physics-informed Koopman network (RFF-PIKN) that directly minimizes the generator loss. We first show that snapshot-based local transition fitting has inherent limitations in long-horizon stability relative to generator-based learning. We then prove that RFF-PIKN converges stably to a local minimizer of the true population risk under the generator loss. Finally, empirical comparisons demonstrate that RFF-PIKN outperforms MLP- and polynomial-based observables in long-horizon prediction while substantially reducing computation, and further matches key behaviors of oracle kernel-based methods.} }
Endnote
%0 Conference Paper %T Scalable Infinitesimal Generator–Based Koopman Learning for Long-Horizon Prediction %A Minseok Jeong %A SooJean Han %A Hyo-Sang Shin %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-jeong26a %I PMLR %P 1966--1980 %U https://proceedings.mlr.press/v331/jeong26a.html %V 331 %X Koopman operator theory offers a linear representation of nonlinear dynamics and has strong potential for long-horizon prediction. However, most existing methods rely on one-step snapshot fitting and suffer from error accumulation over long rollouts. Prior work has attempted to address this by extending training horizons or using physics-informed, generator-based formulations. Still, these approaches remain limited, partly because they rely on MLP-based observables, whose spectral bias favors low-frequency components. In this paper, we introduce a Random Fourier Feature–lifted physics-informed Koopman network (RFF-PIKN) that directly minimizes the generator loss. We first show that snapshot-based local transition fitting has inherent limitations in long-horizon stability relative to generator-based learning. We then prove that RFF-PIKN converges stably to a local minimizer of the true population risk under the generator loss. Finally, empirical comparisons demonstrate that RFF-PIKN outperforms MLP- and polynomial-based observables in long-horizon prediction while substantially reducing computation, and further matches key behaviors of oracle kernel-based methods.
APA
Jeong, M., Han, S. & Shin, H.. (2026). Scalable Infinitesimal Generator–Based Koopman Learning for Long-Horizon Prediction. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1966-1980 Available from https://proceedings.mlr.press/v331/jeong26a.html.

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