Universal Learning of Nonlinear Dynamics

Evan Dogariu, Anand Paresh Brahmbhatt, Elad Hazan
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:25720-25762, 2026.

Abstract

We study the fundamental problem of one-step prediction of a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonexpansive nonlinear dynamical system with finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-dogariu26a, title = {Universal Learning of Nonlinear Dynamics}, author = {Dogariu, Evan and Brahmbhatt, Anand Paresh and Hazan, Elad}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {25720--25762}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/dogariu26a/dogariu26a.pdf}, url = {https://proceedings.mlr.press/v306/dogariu26a.html}, abstract = {We study the fundamental problem of one-step prediction of a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonexpansive nonlinear dynamical system with finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.} }
Endnote
%0 Conference Paper %T Universal Learning of Nonlinear Dynamics %A Evan Dogariu %A Anand Paresh Brahmbhatt %A Elad Hazan %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-dogariu26a %I PMLR %P 25720--25762 %U https://proceedings.mlr.press/v306/dogariu26a.html %V 306 %X We study the fundamental problem of one-step prediction of a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonexpansive nonlinear dynamical system with finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.
APA
Dogariu, E., Brahmbhatt, A.P. & Hazan, E.. (2026). Universal Learning of Nonlinear Dynamics. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:25720-25762 Available from https://proceedings.mlr.press/v306/dogariu26a.html.

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