# Sample Complexity for Nonlinear Dynamics

arXiv: https://arxiv.org/abs/1810.11747 · HTML: https://mlsanity.com/paper/1810.11747/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [One-Step Offline Distillation of Diffusion-based Models via Koopman Modeling](https://mlsanity.com/paper/2505.13358/) (2025)

## Abstract (arXiv)

We consider the identification problems for nonlinear dynamical systems. An explicit sample complexity bound in terms of the number of data points required to recover the models accurately is derived. Our results extend recent sample complexity results for linear dynamics. Our approach for obtaining sample complexity bounds for nonlinear dynamics relies on a linear, albeit infinite dimensional, representation of nonlinear dynamics provided by Koopman and Perron-Frobenius operator. We exploit the linear property of these operators to derive the sample complexity bounds. Such complexity bounds will play a significant role in data-driven learning and control of nonlinear dynamics. Several numerical examples are provided to highlight our theory.