PreprintarXiv licencearXiv
Dynamic models with p parameters are identified by 2p+1 random features
Abstract
A foundational principle in nonlinear dynamics is that the structure of a dynamical system can be recovered from a small number of generic measurements or coordinates. We develop an analogous principle for the identification of dynamic models for time series \textit{with noise}, which builds on previous identification results for noiseless dynamical systems. The noise is allowed to be non-iid, non-Gaussian, and dependent on the state. Our results cover noisily observed differential equations and discrete-time dynamical systems, as well as stochastic models with process noise. We illustrate the utility of this identification principle using a Lorenz-63 model and a Hénon map model, both with observational noise.
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BibTeX
@misc{wiecksosa2026dynamic,
title = {{Dynamic models with $p$ parameters are identified by $2p+1$ random features}},
author = {Michael Wieck-Sosa and Cosma Rohilla Shalizi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.16035},
eprint = {2607.16035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16035},
}
RIS
TY - UNPB
TI - Dynamic models with p parameters are identified by 2p+1 random features
AU - Michael Wieck-Sosa
AU - Cosma Rohilla Shalizi
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2607.16035
UR - https://arxiv.org/abs/2607.16035
AB - A foundational principle in nonlinear dynamics is that the structure of a dynamical system can be recovered from a small number of generic measurements or coordinates. We develop an analogous principle for the identification of dynamic models for time series \textit{with noise}, which builds on previous identification results for noiseless dynamical systems. The noise is allowed to be non-iid, non-Gaussian, and dependent on the state. Our results cover noisily observed differential equations and discrete-time dynamical systems, as well as stochastic models with process noise. We illustrate the utility of this identification principle using a Lorenz-63 model and a Hénon map model, both with observational noise.
ER -