Dynamic models with $p$ parameters are identified by $2p+1$ random features

Michael Wieck-Sosa; Cosma Rohilla Shalizi

Dynamic models with $p$ parameters are identified by $2p+1$ random features

Methodology 2026-07-17 v1 Dynamical Systems Probability Chaotic Dynamics Data Analysis, Statistics and Probability

Authors: Michael Wieck-Sosa , Cosma Rohilla Shalizi

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 {\em 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 H\'{e}non map model, both with observational noise.

Cite

@article{arxiv.2607.16035,
  title  = {Dynamic models with $p$ parameters are identified by $2p+1$ random features},
  author = {Michael Wieck-Sosa and Cosma Rohilla Shalizi},
  journal= {arXiv preprint arXiv:2607.16035},
  year   = {2026}
}