[2508.11990] Universal Learning of Nonlinear Dynamics

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Computer Science > Machine Learning

arXiv:2508.11990 (cs)

[Submitted on 16 Aug 2025]

Title:Universal Learning of Nonlinear Dynamics

Authors:Evan Dogariu, Anand Brahmbhatt, Elad Hazan<br>View a PDF of the paper titled Universal Learning of Nonlinear Dynamics, by Evan Dogariu and 1 other authors

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Abstract:We study the fundamental problem of learning 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 nonlinear dynamical system that has 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 significantly generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.

Subjects:

Machine Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML)

Cite as:<br>arXiv:2508.11990 [cs.LG]

(or<br>arXiv:2508.11990v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2508.11990

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arXiv-issued DOI via DataCite

Submission history<br>From: Anand Brahmbhatt [view email]<br>[v1]<br>Sat, 16 Aug 2025 09:14:47 UTC (4,365 KB)

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