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

2026/07/17 by Michael Wieck-Sosa, Cosma Rohilla Shalizi · 1 voice
#stat.ME #math.DS #math.PR #nlin.CD #physics.data-an

paper · pdf

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 Hénon map model, both with observational noise.

Citations

• Deterministic Nonperiodic Flow
• Analytic extensions of differentiable functions defined in closed sets

Discussions

• Elsewhere: Dynamic models with $p$ parameters are identified by $2p+1$ random features arxiv.org/abs/2607.16035 [bsky, 3 points, 0 comments]

Related

• Estimating dynamic models by matching random features
• Efficient identification of linear, parameter-varying, and nonlinear systems with noise models
• Noise-Aware System Identification for High-Dimensional Stochastic Dynamics
• Dynamic relations in sampled processes
• Identification of Impulse Response Functions for Nonlinear Dynamic Models