# A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems

arXiv: https://arxiv.org/abs/2204.14021 · HTML: https://mlsanity.com/paper/2204.14021/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2022.

## Built on by (most cited first, 3 of 3)

- [Time-Aware World Model for Adaptive Prediction and Control](https://mlsanity.com/paper/2506.08441/) (2025)
- [Tensor-based computation of the Koopman generator via operator logarithm](https://mlsanity.com/paper/2604.07685/) (2026)
- [When Can World Models Recover Physical Laws?](https://mlsanity.com/paper/2610.06877/) (2026)

## Abstract (arXiv)

Low sampling frequency challenges the exact identification of the continuous-time (CT) dynamical system from sampled data, even when its model is identifiable. The necessary and sufficient condition is proposed -- which is built from Koopman operator -- to the exact identification of the CT system from sampled data. The condition gives a Nyquist-Shannon-like critical frequency for exact identification of CT nonlinear dynamical systems with Koopman invariant subspaces: 1) it establishes a sufficient condition for a sampling frequency that permits a discretized sequence of samples to discover the underlying system and 2) it also establishes a necessary condition for a sampling frequency that leads to system aliasing that the underlying system is indistinguishable; and 3) the original CT signal does not have to be band-limited as required in the Nyquist-Shannon Theorem. The theoretical criterion has been demonstrated on a number of simulated examples, including linear systems, nonlinear systems with equilibria, and limit cycles.